Abstract: Traditional convex optimization method cannot find the global maximum since the object function of the direct position determination (DPD) is non-convex, thus, the exhaustive search is usually applied to find the global maximum inefficiently. An efficient method of position estimation with DIRECT (Dividing rectangles) algorithm is employed to solve this problem. Firstly, the received signal model of passive radar with opportunistic illuminator is built, and the object function of DPD is derived with maximum likelihood criterion. Then the DIRECT algorithm is employed to estimate the target position effectively in order to solve the problem that the object function is non-convex and difficult to obtain the global optimal solution, and the computational complexity is analyzed theoretically. Simulation results show that the proposed algorithm can estimate the target position efficiently with high accuracy, and its computation cost is less by two orders of magnitude than the grid search method, and less by one order of magnitude than genetic algorithms.