The best expression is:
'It has a twenty-year history.'
Note that that 'twenty-year' is used as an adjective here, and the word 'year' is in the singular. Not 'years', but 'year'.
2015년 5월 24일
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You could also say :
It has a/an x-year history e.g. a 20-year history.
They both mean the same but this version is more concise.