Aiming at obtaining multiple types of coexisting attractors, a new four-dimensional dissipative chaotic system with multi-stability was constructed. The system’s dynamic behavior was analyzed through the numerical simulations of phase diagrams, Lyapunov exponents, bifurcation diagram, etc. An analog circuit of the system was designed and simulated by the Multisim software. And a digital FPGA (Field Programmable Gate Array) circuit of the system was also designed. The simulation results of the two kinds of circuit were consistent with each other, which verified the system’s chaotic behavior and its implementability. The system has some important characteristics, such as for different values of system parameters, there are ten types of coexistence of attractors in the system. The involved coexisting attractors are point attractors, different periodic attractors, quasi-periodic attractors, and different chaotic attractors. The system’s characteristics have strong sensitivity to parameters, which means there are frequent switches between the periodic state and the chaotic state with the varied parameters. The topologies of the system’s attractors are dominated by the parameters, which means there are one-scroll attractors, two-scroll attractors, and four-scroll attractors in the system corresponding to different values of the parameters.