A Hybrid Particle Swarm Optimization (HPSO) algorithm is proposed to optimize the Radial Basis Function Neural Network (RBFNN) for the image reconstruction of Electrical Impedance Tomography (EIT). This algorithm combines the non-linear approximation ability of RBFNN with the mutation ability of HPSO based on the simulated annealing, which has advantages of the strong global search ability and high robustness. A non-linear mapping relationship model between the boundary voltage and the conductivity distribution is established through HPSO-RBFNN to realize the image reconstruction, skipping the solution of the Jacobian matrix. The Structural similarity (SS) and correlation coefficient (CC) are used as the evaluation criteria for the quality of the reconstructed images in the simulations and experiments. Firstly, the HPSO-RBFNN method is compared with the Landweber and RBFNN methods through a single-target simulation, which verifies the accuracy of the image reconstruction. Secondly, the Gaussian noise is added to the ideal simulation data, the results show an anti-noise capability of the proposed method. Then, the multi-target simulation is conducted using the single-target training model, which verifies the generalization ability of the proposed method. Finally, the experiments with multiple fish eggs are performed to further verify the effectiveness of the HPSO-RBFNN method. The results show that the method proposed in this article has higher SS and CC, which indicates that the HPSO-RBFNN method has a higher accuracy.