In this paper, we construct a cost constrained spatial network by adding long-range connections to the one-dimensional circle. The probability for a long-range connection between nodes i and j is pij dij- ( 0), where dij is the lattice distance and the total length of the long-range connections is set to be =cN(c 0), where c is a positive constant and N is the network size. According to the simulation and numeric results, we find an optimal power-law exponent 0 such that the mean first-passage time is shortest. Furthermore, the shortest mean first-passage time has the power law relationships with the network size N. With the increase of network size N and the total cost , the optimal power-law exponent 0 increases monotonically and approaches 1.5.