Sensor network localization (SNL) has been an important subject of research in recent years for a wide variety of applications. Among the solution methods proposed for SNL problems, semidefinite programming (SDP) approach is known for its effectiveness of obtaining solutions. In particular, the full SDP (FSDP) relaxation by Biswas and Ye was shown to be successful for solving small to medium-sized SNL problems. We present a sparse version of FSDP (SFSDP) for larger-sized problems by exploiting the sparsity of the problem. This method finds the same quality of solutions as the FSDP in a shorter amount of time. The performance of the SFSDP is measured with randomly generated test problems and compared with other methods. Numerical results suggest that exploiting the sparsity of the problem improve the efficiency of solving largersized problems.