The cooperative localization technique using relative range measurement information between a leader and a follower AUV can significantly improve the overall localization accuracy of the multiple AUV team. For the influence of the multiple AUV formation geometry on the performance of cooperative localization, the logarithms of determinants of Fisher information matrices(FIM) are used to generate an evaluation criterion for the performance of cooperative localization, which can be maximized to derive the optimal formation geometry.When the multiple AUV team consists of two follower AUVs or more than two concyclic follower AUVs, the optimal formation geometry for cooperative localization is analyzed and verified.A gradient descent algorithm is designed to iteratively seek the optimization formation in the case of more than two non-concyclic follower AUVs.Simulation results show the effectiveness of analytical results and the practicality of the proposed formation optimization algorithm.