Based on quadratic programming-unscented Kalman filter(QP-UKF) and multidimensional scaling-MAP (MDS-MAP) methods, this paper studies localization problem for the mobile sensor network with high accuracy. From the perspective of overall localization for the wireless sensor network, a new idea of mobile sensor network localization is provided. Firstly, a nonlinear dynamic relative motion model is established for sensor network units according to practical condition. By considering the constraints in the established model, the QP-UKF is introduced to estimate the actual ranges among nodes in each senor network unit. Then, based on the MDS-MAP method and estimated ranges, the whole mobile sensor network can be localized through clustering, local-localizing and merging. Finally, a complete range-based localization algorithm is proposed for the mobile sensor network with incomplete measurement. Several simulation examples illustrate that with the same range error ratio, the localization accuracy of the proposed algorithm is higher than the existing algorithms, and can perform well for the mobile sensor network with different connectivity.