The geometric dilution of precision is widely used as criterion for selecting the best set of the measurement devices. Some methods had been proposed to rmd the value of the Geometric Dilution of Precision (GDOP), such as using inverse matrix to solve the linear equation. But it takes a large amount of computing time to find the optimal solution. In this paper, we propose to adopt a neural network with gradient descent adaptive learning rate training algorithm to approximate the value of GDOP. The proposed two types of input/output mapping used the element in the matrix as the input data of the neural network. After finishing the training process, it can get a better approximation results with the proposed two types. The simulation result shows that proposed algorithm has lower GDOP approximation error using less Epochs than the other types. For cellular wireless communication system, it will significantly reduce the computational complexity and the training time by selecting the service base station at first with three other base stations to estimate the position of mobile station.