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The Government has so far approved 89 golf courses nationwide until 2020.
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I am confused with the using of "until 2020" here. Is the phrase used correctly?
I think it needs to add something like this:
The Government has so far approved 89 golf courses nationwide which will be built until 2020.
Is this sentence correct?
You are right in thinking that the original sentence is incorrect. However, you have also used "until" wrongly. Your sentence implies that there will be absolutely no more golf courses built after 2020. It would be better to replace "until" with "by", as in "The Government has so far approved the construction of 89 golf courses nationwide by 2020". That leaves the option open of approving the construction of more golf courses in the future.
I'm not a teacher of English, but I have spoken it for (almost) all of my life....