The early diagnosis of sepsis reduces the risk of the patient's death. Gradient-based algorithms are applied to the neural network models used in the estimation of sepsis in the literature. However, these algorithms become stuck at the local minimum in solution space. In recent years, swarm intelligence and an evolutionary approach have shown proper results. In this study, a novel hybrid metaheuristic algorithm was proposed for optimization with regard to the weights of the deep neural network and applied for the early diagnosis of sepsis. The proposed algorithm aims to reach the global minimum with a local search strategy capable of exploring and exploiting particles in Particle Swarm Optimization (PSO) and using the mental search operator of the Human Mental Search algorithm (HMS). The benchmark functions utilized to compare the performance of HMS, PSO, and HMS-PSO revealed that the proposed approach is more reliable, durable, and adjustable than other applied algorithms. HMS-PSO is integrated with a deep neural network (HMS-PSO-DNN). The study focused on predicting sepsis with HMS-PSO-DNN, utilizing a dataset of 640 patients aged 18 to 60. The HMS-PSO-DNN model gave a better mean squared error (MSE) result than other algorithms in terms of accuracy, robustness, and performance. We obtained the MSE value of 0.22 with 30 independent runs.