Your essay is clearly organized. However, you have some long sentences which I would shorten, and you could make some of your ideas a little simpler.

Long sentences:

Thus affordable airfare may be an ideal choice in line with cost-effectiveness for common people to travel and enjoy advantages of air travel, such as long distance, time-saving or fast speed and so forth. (36 words)

I would shorten and simplify this to

Affordable airfares allow ordinary people to save time and travel long distances. (12 words)

Here's another long sentence:

More significantly, cheap air travel plays a praiseworthy role in wiping out the inferiority complex in all walks of life that merely upper class had been financially capable of taking a flight previously. (33 words)

I might shorten and simplify this to:

Cheap air travel can be praised for wiping out the unfair distinction between ordinary people and the upper class, the only ones able to fly previously. (26 words)

I generally recommend that your average sentence length should be about 12 words. This means a mix of short and long sentences, but you should definitely try to keep sentences shorter than 30 words. If you have 20 sentences with an average 12 words, that's about 240 words - perfect for IELTS!  Writing longer sentences increases the chance of errors in agreement and syntax.

Simplify some ideas:

Your ideas are excellent, but could be a little clearer if they were expressed more simply. Some sentences are very dense and require a lot of work for the reader. In IELTS, the writer's task is to make it easy for the reader, not necessarily to compose beautiful or intricate sentences and paragraphs.

Here's one idea I might clarify or simplify a little:

The increase in demand of air cheap travel inevitably results in high frequencies of airlines that are associated with environment concerns.

Here are two suggestions

As more cheap airlines appear, there are more environmental concerns over the pollution caused by flying.

or

As they compete for passengers, some cheap airlines may less attention to environmental issues.

Consider using more verbs and fewer nouns in your sentences.

I look forward to seeing more writing from you!

These days, it is widely accepted that air travel benefits not only international transportation but also its passengers by offering convenient travelling services on a wide variety of charge. Particularly, it is easy for ordinary people to book and enjoy their flights economically. However, others dispute on environmental hazard which is currently posed to our planet by cheap air travel. This essay will discuss both advantages and disadvantages of low-cost air carriers.

          Due to vigorous development of aviation, airways constantly continue to expand their market by providing low-cost air carrier for low-income passengers. Thus affordable airfare may be an ideal choice in line with cost-effectiveness for common people to travel and enjoy advantages of air travel, such as long distance, time-saving or fast speed and so forth. Travel expenses will no longer be viewed as a huge barrier to low-income class and air travel shall be more acessible than ever. More significantly, cheap air travel plays a praiseworthy role in wiping out the inferiority complex in all walks of life that merely upper class had been financially capable of taking a flight previously.

          In other words, there is a pressing need to sufficiently measure environmental impacts of air cheap travel. The increase in demand of air cheap travel inevitably results in high frequencies of airlines that are associated with environment concerns. Futhermore, deforestration and river clearance to offer space for airport expansion or news airports still stir deep public concerns among its ecological influences.  Most importantly, there has been some study claiming that air plane consume the largest amount of fuel thus produce huge quantities of emission of carbon dioxite and other toxics to our nature. Therefore, low-cost air carriers certainly put national administration under pressures to balance its enormous benefits against the environmental effect.

          In my view, the necessity of cheap air travel is undeniable in modern world. However, inevitable environment impacts of low-cost travel should be cautiously taken into account and sorted out effectively to perfect this beneficial business. 

Thanks for your attention. Please correct mistakes in my essay and tell me what you think of it. Thanks so much again ! :D