Several engineering problems involve simultaneously several objective functions where at least one of them is expensive to evaluate. This fact has yielded to a new class of Multi-Objective Problems (MOPs) called expensive MOPs. Several attempts have been conducted in the literature with the goal to minimize the number of expensive evaluations by using surrogate models stemming from the machine learning field. Usually, researchers substitute the expensive objective function evaluation by an estimation drawn from the used surrogate. In this paper, we propose a new way to tackle expensive MOPs. The main idea is to use Neural Networks (NNs) within the Indicator-Based Evolutionary Algorithm (IBEA) in order to estimate the contribution of each generated offspring in terms of hypervolume. After that, only fit individuals with respect to the estimations are exactly evaluated. Our proposed algorithm called NN-SS-IBEA (Neural Networks assisted Steady State IBEA) have been demonstrated to provide good performance with a low number of function evaluations when compared against the original IBEA and MOEA/D-RBF on a set of benchmark problems in addition to the airfoil design problem.