This paper proposes a neural network approach to efficiently solve nonlinear convex programs with the second-order cone constraints. The neural network model is designed by the generalized FischerBurmeister function associated with second-order cone. We study the existence and convergence of the trajectory for the considered neural network. Moreover, we also show stability properties for the considered neural network, including the Lyapunov stability, the asymptotic stability and the exponential stability. Illustrative examples give a further demonstration for the effectiveness of the proposed neural network. Numerical performance based on the parameter being perturbed and numerical comparison with other neural network models are also provided. In overall, our model performs better than two comparative methods.