This paper aims at improving the performance of MPI broadcasts under unbalanced process arrival (UPA) patterns. This paper analyzes this problem with a performance model and proves that the negative impact of UPA on MPI broadcast can be effectively reduced by the competition of intra-node MPI processes on a multicore cluster. Based on this theory, a new optimizing method, called competitive and pipelined method (CP), is proposed. The CP method can start inter-node communications during the broadcast process through an intra-node competitive mechanism. In a CP method based broadcast algorithm, intra-node communications overlap inter-node communications through a pipelined method, and intra-node communications are implemented through shared memory while inter-node communications are executed by a set of leader MPI processes, which is selected by the competitive mechanism. In order to verify the CP method, this paper improves three typical broadcast algorithms by using this method and evaluates these algorithms in a real platform by using a micro-benchmark case and two practical applications. The results show that the performance of the CP method can effectively improve the performance of broadcast algorithms in the condition of UPA patterns. In the experimental results of the performance of the practical applications, the performance of CP broadcasts is about 16% higher than the performance of P broadcasts and is 18% to 24% higher than the performance of broadcast operation in MVAPICH2 1.2.