In this letter, the moving target localization problem is studied under distributed multiple-input multiple-output radar systems. Based on the two-stage weighted least squares framework, a closed-form solution of target position and velocity is derived. In the first stage, linear equations about target position and velocity are established with no nuisance parameters. Then the estimate is achieved by a weighted least squares (WLS) estimator. In the second stage, the estimation error of the first stage is estimated by another WLS method to refine the localization performance. The final estimate, combining solutions of the first stage and the second stage, is approximately unbiased and its covariance is equal to the Cramer-Rao lower bound under small noise conditions through the theoretical derivation and numerical simulations. Simulation results demonstrate the proposed method achieves better location accuracy than the state-of-the-art algorithms.