Neural networks, combined with implicit polynomials, can be employed to represent 3D surfaces which are described by the zero-set of a neural network. First, an explicit function is constructed based on the implicit function. Then the explicit function is approximated by a BP neural network. Finally, the zero-set of the neural network which is the implicit surface is extracted from the simulation surface. The method is not sensitive to the error, the number of the constraint points, and the distance between the boundary points and inner/extern points. Experimental results are given to verify the effectiveness of surface reconstruction.