The assay and recovery of rare earth elements (REEs) in the leaching process is being determined using expensive analytical methods: inductively coupled plasma atomic emission spectroscopy (ICP-AES) and inductively coupled plasma mass spectroscopy (ICP-MS). A neural network model to predict the effects of operational variables on the lanthanum, cerium, yttrium, and neodymium recovery in the leaching of apatite concentrate is presented in this article. The effects of leaching time (10 to 40 min), pulp densities (30% to 50%), acid concentrations (20% to 60%), and agitation rates (100 to 200 r/min), were investigated and optimized on the recovery of REEs in the laboratory at a leaching temperature of 60°C. The obtained data in the laboratory optimization process were used for training and testing the neural network. The feed-forward artificial neural network with a 4-5-5-1 arrangement was capable of estimating the leaching recovery of REEs. The neural network predicted values were in good agreement with the experimental results. The correlations of R=1 in training stages, and R=0.971, 0.952, 0.985, and 0.98 in testing stages were a result of Ce, Nd, La, and Y recovery prediction respectively, and these values were usually acceptable. It was shown that the proposed neural network model accurately reproduced all the effects of the operation variables, and could be used in the simulation of a leaching plant for REEs.