Mobile location estimation has attracted a significant amount of attention in recent years. The network-based location estimation schemes have been widely adopted based on the radio signals between the mobile device and the base stations. The two-step Least-Squares (LS) method has been studied in related research to provide efficient location estimation of the mobile devices. However, the algorithm results in insufficient accuracy for location estimation with the existence of Non-Line-Of-Sight (NLOS) errors. A Geometry-Assisted Location Estimation (GALE) algorithm is proposed in this paper with the consideration of different geometric layouts between the mobile device and its associated base stations. In order to enhance the precision of the location estimate, the GALE scheme is designed to incorporate the geometric constraints within the formulation of the two-step LS method. The algorithm can be utilized to estimate both the two-dimensional and the three-dimensional positions of a mobile device. The proposed GALE scheme can both preserve the computational efficiency from the two-step LS algorithm and obtain a precise location estimation under NLOS environments. Moreover, the Cramér-Rao Lower Bound (CRLB) for various types of measurement signals is derived to facilitate the performance comparison between different location estimation schemes. Numerical results illustrate that the proposed GALE algorithm can achieve better accuracy compared with other existing network-based location estimation schemes.