This paper surveys the artificial neural networks approach. Researchers believe that these networks have the wide range of applicability, they can treat complicated problems as well. The work described here discusses an efficient computational method that can treat complicated problems. The paper intends to introduce an efficient computational method which can be applied to approximate solution of the linear two-dimensional Fredholm integral equation of the second kind. For this aim, a perceptron model based on artificial neural networks is introduced. At first, the unknown bivariate function is replaced by a multilayer perceptron neural net and also a cost function to be minimized is defined. Then a famous learning technique, namely, the steepest descent method, is employed to adjust the parameters (the weights and biases) to optimize their behavior. The article also examines application of the method which turns to be so accurate and efficient. It concludes with a survey of an example in order to investigate the accuracy of the proposed method.