In this paper, we propose an efficient batch Bayesian optimization algorithm for analog circuit synthesis based on the multi-points selection criterion. Simplex evolution operator and Niching Migratory Multi-Swarm Optimizer (NMMSO) are used to generate candidates. The multi-point selection criterion is adopted to select multiple points from the candidates for parallel evaluation which can make full use of the computing resources. The experimental results demonstrate that this method can reduce the simulation time effectively while achieving better optimization results. Compared with the Multi-objective Acquisition function Ensemble (MACE) and the weighted expected improvement based Bayesian optimization (WEIBO), our proposed approach can accelerate the optimization process by up to 3× and 27×