In this paper, we solved a non-linear differential equations of the second order Lane–Emden equation using the neural network method based on shifted Legendre polynomial. The proposed problems are classified as initial value problems with singularities. To manage the challenge of singularity, we implement an artificial neural network method. The implemented approach utilizes neural network of a single-layer, where the hidden layer is omitted by enlarge the input using the approximation with shifted Legendre polynomials. Also, we implement a feed-forward neural network model along with the principle of error back propagation. Moreover, the effectiveness of the artificial neural network method based on shifted Legendre polynomial is demonstrated through Lane–Emden equations.