Abstract: The normal gravity aided navigation theories are based on grid discrete field in most cases. It is indispensable to build the local continuous gravity anomaly field model with high precision and good analytic property before the study on gravity matching algorithm based on continuous field. Fibonacci series searching is applied to optimize the 1-D Gauss spline function interpolation and the algorithm to approximate the local grid gravity anomaly field with the 2-D Gauss spline function based on Fibonacci series search is put forward. To improve the searching speed, the 2-D criterion function was decoupled to two mutually independent 1-D criterion functions at the X and Y direction. Then, the optimal parameters were obtained from the Fibonacci number series searching of these two 1-D criterion functions. Finally, a local continuous gravity anomaly field analytic model which can approximate to local grid data with high precision is attained. Five different parameters were set in the simulation to approximate the gravity anomaly with the variation range -51.185mGal~86.1819mGal. The simulation results shows that approximation mean absolute error of the simulation with optimal parameters is 0.00069 and the mean relative error is to the level of 10-6 which is far less than the simulations with the other parameters. The effectiveness of the reconstruction algorithm was proved by the simulation results and the approximating precision can satisfy the need of matching navigation.