Though label propagation algorithm (LPA) is one of the fastest algorithms for community detection in complex networks, the problem of trivial solutions frequently occurring in the algorithm affects its performance. We propose a label propagation algorithm with prediction of percolation transition (LPAp). After analyzing the reason for multiple solutions of LPA, by transforming the process of community detection into network construction process, a trivial solution in label propagation is considered as a giant component in the percolation transition. We add a prediction process of percolation transition in label propagation to delay the occurrence of trivial solutions, which makes small communities easier to be found. We also give an incomplete update condition which considers both neighbor purity and the contribution of small degree vertices to community detection to reduce the computation time of LPAp. Numerical tests are conducted. Experimental results on synthetic networks and real-world networks show that the LPAp is more accurate, more sensitive to small community, and has the ability to identify a single community structure. Moreover, LPAp with the incomplete update process can use less computation time than LPA, nearly without modularity loss.