Hydrogen purification from steam methane reforming (SMR) by pressure swing adsorption (PSA) technology is a common method to obtain high-purity hydrogen. The breakthrough time can well reflect the adsorption dynamics and help PSA cycle design. In order to avoid time-consuming and labor-intensive breakthrough curve experiments, it is very necessary to develop a fast and accurate surrogate model. In this study, a genetic algorithm (GA) and artificial neural network (ANN) are combined to predict and optimize breakthrough times of adsorbates in activated carbon/zeolite layered beds. Using the Latin hypercube sampling strategy, training data sets of GA-optimized ANN (GA-ANN) obtains from the physical model of adsorption, heat and mass transfer model. The genetic algorithm (GA) optimizes the weights and biases of ANN for better performance. The ANN topology has 4 input variables (superficial velocity, activated carbon height, adsorption pressure and feed temperature) and 3 output variables (breakthrough times of CH4, CO and CO2). The number of neurons in the hidden layer for the GA-ANN model was optimized as 7 to predict and optimize the maximum breakthrough time of SMR with a four-component (H2/CH4/CO/CO2) system. The sensitivity analysis displays that relative importance to the breakthrough time is in the order of superficial velocity (40.88%) > adsorption pressure (24.55%) > activated carbon height (21.04%) > feed temperature (13.53%). To obtain high-purity hydrogen, the GA-ANN model combined with multi-objective GA optimization is used to maximize the breakthrough times of CH4 and CO. The GA-ANN surrogate model proposed in this paper can not only accurately and quickly achieve the purpose of predicting the system breakthrough time with a high correlation coefficient (R = 0.9937) but also obtains the optimal operating conditions of PSA hydrogen purification.