This paper proposes an improved closed-form method for moving source localization using time difference of arrival (TDOA), frequency difference of arrival (FDOA) and differential Doppler rate measurements. After linearizing the measurement equations by introducing three additional parameters, a rough estimate is obtained by using the weighted least-square (WLS) estimator. To further refine the estimate, the relationship between additional parameters and source location is utilized. The proposed method gives a final closed-form solution without iteration or the extra mathematics operations used in existing methods by employing the basic idea of WLS processing. Numerical examples show that the proposed method exhibits better robustness and performance compared with several existing methods.