The Fintech index has been more active in the stock market with the Fintech industry expanding. The prediction of the Fintech index is significant as it is capable of instructing investors to avoid risks and provide guidance for financial regulators. Traditional prediction methods adopt the deep neural network (DNN) or the combination of genetic algorithm (GA) and DNN mostly. However, heavy computational load is required by these algorithms. In this paper, we propose an integrated artificial intelligence‐based algorithm, consisting of the random frog algorithm (RF), GA, and DNN, to predict the Fintech index. The proposed RF‐GA‐DNN prediction algorithm filters the key input variables and optimizes the hyperparameters of DNN. We compare the proposed RF‐GA‐DNN with the traditional GA‐DNN in terms of convergence time and prediction accuracy. Results show that the convergence time of GA‐DNN is up to 20 hours and its prediction accuracy is 97.4%. In comparison, the convergence time of our RF‐GA‐DNN is only about 1.5 hours and the prediction accuracy reaches 97.0%. These results demonstrate that the proposed RF‐GA‐DNN prediction algorithm significantly reduces the convergence time with the promise of competitive prediction accuracy. Thus, the proposed algorithm deserves to be widely recommended for predicting the Fintech index.