Evolutionary multi-objective optimization of spiking neural networks for solving classification problems is studied in this paper. By means of a Pareto-based multi-objective genetic algorithm, we are able to optimize both classification performance and connectivity of spiking neural networks with the latency coding. During optimization, the connectivity between two neurons, i.e., whether two neurons are connected, and if connected, both weight and delay between the two neurons, are evolved. We minimize the the classification error in percentage or the root mean square error for optimizing performance, and minimize the number of connections or the sum of delays for connectivity to investigate the influence of the objectives on the performance and connectivity of spiking neural networks. Simulation results on two benchmarks show that Pareto-based evolutionary optimization of spiking neural networks is able to offer a deeper insight into the properties of the spiking neural networks and the problem at hand.