<p>Newton’s method is a classic technique to solve systems of nonlinear equations known for its rapid convergence. However, the choice of initial values has a significant impact on the convergence speed of Newton’s method and whether it can converge to the correct solution. In the study, a new technique which combines radial basis function neural network (RBFNN) with Newton’s method to solve systems of nonlinear equations is proposed. Employing RBFNN to learn a more appropriate initial value can decrease the number of iterations for solving systems of nonlinear equations through Newton’s method. Meanwhile, it is theoretically demonstrated that RBFNN has the ability to offer an outstanding initial value for Newton’s method. Also, it is proved that using the output value of the RBFNN as a new initial value can make Newton’s method converge to the correct solution faster. Finally, the effectiveness of our technique is verified by several benchmark numerical examples. At the same time, when the dimension of systems of nonlinear equations is relatively large, the solution speed of our technique is faster than that of the RBFNN method alone and Newton’s method alone. For example, for a 100-dimensional system of nonlinear equations, the efficiency of our technique is twice that of Newton’s method.</p>