Due to the complex chemical composition of nickel ores, the requests for the decrease of production costs, and the increase of nickel extraction in the existing depletion of high-grade sulfide ores around the world, computer modeling of nickel ore leaching process became a need and a challenge. In this paper, the design of experiments (DOE) theory was used to determine the optimal experimental design plan matrix based on the D optimality criterion. In the high-pressure sulfuric acid leaching (HPSAL) process for nickel laterite in "Rudjinci" ore in Serbia, the temperature, the sulfuric acid to ore ratio, the stirring speed, and the leaching time as the predictor variables, and the degree of nickel extraction as the response have been considered. To model the process, the multiple linear regression (MLR) and response surface method (RSM), together with the two-level and four-factor full factorial central composite design (CCD) plan, were used. The proposed regression models have not been proven adequate. Therefore, the artificial neural network (ANN) approach with the same experimental plan was used in order to reduce operational costs, give a better modeling accuracy, and provide a more successful process optimization. The model is based on the multi-layer neural networks with the back-propagation (BP) learning algorithm and the bipolar sigmoid activation function.