In this paper, we consider a randomized greedy algorithm for independent sets in -uniform -regular hypergraphs on vertices with girth . By analyzing the expected size of the independent sets generated by this algorithm, we show that , where converges to as for fixed and , and is determined by a differential equation. This extends earlier results of Gamarnik and Goldberg for graphs~\cite{GG}. We also prove that when applying this algorithm to uniform linear hypergraphs with bounded degree, the size of the independent sets generated by this algorithm concentrate around the mean asymptotically almost surely.