In this paper, a distributed localization algorithm is designed to copes with the multi-agent target localization problem under switching topology, which can estimate the relative position of the silent target in each agent's local frame. Agents can only detect local measurements and exchange local information. The whole algorithm includes two parts: the algorithm for relative localization between pairwise agents, and the consensus-like fusion target localization algorithm based on the pairwise localization algorithm. The rigorous analysis for the topology condition and convergence of estimate error is presented. Simulation with and without measurement noises are also carried out to verify the effectiveness of the proposed algorithms.