To construct a complex four-dimensional hyperchaotic system with chaotic characteristics and to improve the security of image data protection a four-dimensional hyperchaotic system with only one equilibrium point by introducing a state feedback controller based on the classical system Lü was proposed and constructed. The dynamics of the four-dimensional hyperchaotic system was analyzed theoretically and a hyperchaotic encryption algorithm to protect the data security after image encryption was designed. Methods Numerical simulations of this hyperchaotic system such as system dissipation and equilibrium point stability Lyapunov exponential spectrum and bifurcation diagram and Poincare cross-section were performed using Matlab software. Meanwhile the simulation circuit of the four-dimensional hyperchaotic system was designed and the simulation circuit model of the hyperchaotic system was built based on the operational amplifier circuit through the basic circuit components. Finally the four-dimensional hyperchaotic system is combined with the dislocation-diffusion algorithm to design an efficient and secure four-dimensional hyperchaotic image encryption algorithm by using the complexity and pseudo-randomness of the chaotic sequence of the hyperchaotic system and the histogram adjacent pixel correlation information entropy and attack resistance of plaintext and ciphertext images were analyzed by Matlab software. Results Simulation data showed that this four-dimensional hyperchaotic system has complex chaotic behavior with periodic chaotic and hyperchaotic attractors while Multisim software was used to verify the accuracy and physical realizability of the circuit implementation. The experimental data of image encryption show that the super system is very sensitive to chaotic keys and plaintexts and the hyperchaotic encryption algorithm is more secure. Meanwhile it can effectively resist statistical and differential attacks under the premise of ensuring security and it also speeds up image decryption and encryption. Conclusion The experimental conclusion shows that this four-dimensional hyperchaotic system can exhibit complex dynamics under different parameters and the chaotic encryption algorithm designed by using the chaotic sequence generated by the hyperchaotic system has high security.