To solve the problem of fewer beacon nodes and unknown transmission time in Time of Arrival (ToA) based localization, a new linear programming algorithm was proposed to approximate nonlinear localization estimation problems. We consider the least mean absolute errors of the residual and formulate the nonconvex localization problem as a simple linear programming by using linear approximation. Simulation results demonstrate that the proposed algorithm can maintain good positioning accuracy under fewer beacon nodes and achieve better performance by using less node resources than the existing algorithms.