This paper proposes an empirical model of RSSI radio map in order to improve the indoor positioning accuracy of Wi-Fi RSSI. First, the signal feature point in RSSI space is proposed based on the indoor RSSI map, which is similar to the geomorphic feature point in a topographic map. Then, we utilize a small amount of the grid points in geometric space to fill the RSSI grid network by using the theory of low rank matrix. Finally, a new algorithm for indoor RSSI radio map reconstruction has been proposed. Both the grid point in geometric space and the signal feature point in RSSI space have been utilized in the reconstruction of the RSSI empirical model, and different types of feature points have been weighted based on their corresponding positioning accuracy. The proposed algorithm was tested by experiments conducted within a room, and the results indicate that the proposed method significantly outperforms the traditional grid network algorithm.