To obtain compound attractors between different chaotic systems, based on theoretical analysis, numerical simulation, and circuit simulation methods, compound attractors between different 2-scroll systems, between different multi-scroll chaotic systems, between 2-scroll system and 2-wing system and between multi-scroll system and multi-wing system, are designed via switching control. Dynamical characteristics of the system are analyzed by observing the attractor phase diagram, the largest Lyapunov exponent and the Poincaré section. A circuit for a compound multiple scroll-multiple wing chaotic attractor is designed and simulated. Numerical simulation and circuit simulation are consistent with each other. It shows that the method of obtaining compound attractors between different chaotic systems via switching control is correct.