This article proposes a novel MPPT algorithm based on the firefly algorithm and elite ant system-trained Elman neural network (FA-EAS-ElmanNN). First, the position of fireflies is randomly initialized by the firefly algorithm (FA), meanwhile the firefly individuals with higher attractiveness degree value are selected as the optimal solution. Second, the extra pheromones are artificially released to boost the positive feedback effect and convergence rate of the elite ant system (EAS). Third, the weight and threshold of the Elman neural network (ElmanNN) are updated by the FA and EAS. Also, the trained ElamnNN is employed to acquire the maximum voltage of the photovoltaic (PV) array. At last, the PID controller and PWM technology are adapted to regulate the switch time of the boost converter. Furthermore, MATLAB/Simulink is adopted to acquire the datasets of irradiance, temperature, and maximum voltage and validate the reliability and superiority of the proposed algorithm under complex atmospheric conditions. The tracking characteristic, response speed, and efficiency of the proposed MPPT algorithm are contrasted with the particle swarm optimization (PSO), ant colony optimization (ACO), ACO-artificial neural network (ACO-ANN), and PSO-RBF neural network (PSO-RBNFNN) algorithm via simulation. The efficiency of the FA-EAS-ElmanNN algorithm is 99.73%, compared with the ACO-ANN, PSO-RBFNN, PSO, and ACO algorithm, which is increased by 0.49%, 0.58%, 1.2% %, and 1.5%, respectively. Additionally, the experimental setup is built to demonstrate the tracking characteristic of the proposed MPPT algorithm.