This paper presents the application of an artificial neural network (ANN) in order to predict the effects of operational parameters on the dissolution of Cu, Mo and Re from molybdenite concentrate through mesoacidophilic bioleaching. The initial pH, solid concentration, inoculum percent and time (days) were used as inputs to the network. The outputs of the models included the percent of Cu, Mo and Re recovered. The development and training of a feed-forward back-propagation artificial neural network (BPNN) was used to model and predict their recoveries. 105 sets of data were used to develop the neural network architecture and train it. To reach the network with highest generalizability, the space of neural networks with different hidden layers (one up to three hidden layers) and with the varying number of neurons each layer were searched. As a result, it was found that (4-5-5-2-1); (4-7-5-2-1) and (4-7-1-1-1) arrangements could give the most accurate prediction for Cu, Mo and Re extraction respectively. The regression analysis of the models tested gave a good correlation coefficient of 0.99968, 0.99617 and 0.99768 respectively for Cu, Mo and Re recoveries. The results demonstrated that ANN has a good potential to predict Cu, Mo and Re recoveries. Also, genetic algorithm (GA) was used to find out the optimum levels of parameters in the best models defined by ANN. The maximum recovery of Cu, Mo and Re on the 30th day were nearly 73%, 2.8% and 27.17% respectively.