In this paper, a novel variable selection method for neural network that can be applied to describe nonlinear industrial processes is developed. The proposed method is an iterative two-step approach. First, a multilayer perceptron is constructed. Second, the least absolute shrinkage and selection operator is introduced to select the input variables that are truly essential to the model with the shrinkage parameter is determined using a cross-validation method. Then, variables whose input weights are zero are eliminated from the data set. The algorithm is repeated until there is no improvement in the model accuracy. Simulation examples as well as an industrial application in a crude distillation unit are used to validate the proposed algorithm. The results show that the proposed approach can be used to construct a more compressed model, which incorporates a higher level of prediction accuracy than other existing methods.