The problem of selecting a sequence of items from a universe that maximizes some given objective function arises in many real-world applications. In this paper, we propose an anytime randomized iterative approach POSeqSel, which maximizes the given objective function and minimizes the sequence length simultaneously. We prove that for any previously studied objective function, POSeqSel using a reasonable time can always reach or improve the best known approximation guarantee. Empirical results exhibit the superior performance of POSeqSel.