Neural networks have already been successfully applied to model the real world problems. The current research attempts to employ architecture of artificial neural networks for approximating solution of a system of fuzzy equations. For this aim, a multi-layer fuzzified feed-forward neural network (FFNN) on the real connection weights space is used. The proposed neural network architecture is able to approximate the unknowns by using a supervised learning algorithm which is based on the gradient descent method. The given approach has been illustrated by several examples with computer simulations.