The invention discloses a multi-target positioning outer approximation nearly convex optimization algorithm on the basis of arrival time. The multi-target positioning outer approximation nearly convex optimization algorithm includes building original problem models; relaxing original problems by the aid of relaxation methods to obtain a mixed integer convex optimization problem model; constructing novel appropriate constraints for semi-positive definite matrixes; solving coordinate values of various to-be-positioned targets by the aid of outer approximation nearness algorithm sub-models, continuous convex optimization problem models and OAA (open application architecture) algorithms. The multi-target positioning outer approximation nearly convex optimization algorithm has the advantages that complicated requirements of existing methods on layout of base stations and regions where the targets are located can be omitted by outer nearness approximation algorithms, and the global optimal solution can be assuredly converged without initial estimation points.