The value of work was up by 7% compared to the same quarter in 2013.
An increase in house building, up 10.5% on the same period last year, drove the improved performance.
However, the output of the industry is still dramatically below its peak in 2007.
The Construction Bulletin, produced by the Department of Finance, said that "over the last four quarters, construction output appears to have stabilised".
However, it added that it is "too early to say whether this is a part of a sustained recovery".
The bulletin also said that in the past two years, housing output "looks like it may have reached its lowest points".
House building is still around 60% lower than its 2007 peak.
Construction employers welcomed the rise and said it was "positive news for the local industry".
"Overall, 2014 marks the first year since 2007 in which output has not significantly declined year on year," they said.
"It is too early to say for certain, but we firmly hope that this means we have reached the bottom."
The Northern Ireland construction industry had its best performance in almost two years in the last quarter of 2014, official figures have suggested.