The solution methods based on semidefinite programming (SDP) relaxations for sensor network localization (SNL) problems can not handle very large-sized SNL problems. We present a continuation method using the gradient descent method to efficiently solve large-sized SNL problems. We first formulate the problem as an unconstrained optimization problem and then apply the continuation on the distance information with the continuation parameter. We show numerically that the continuation method provides an approximate solution efficiently with comparable accuracy to that of SFSDP, a Matlab software package, which showed better performance than other SDP-based methods for solving various types of the problems. Numerical results are presented to illustrate the performance of the proposed method in comparison with SFSDP.