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Based on the Si' lnikov theorem, this paper proposed a new three-dimensional square chaotic system, which had tow equilibrium poits. There was hyperbolic saddle focus. The formation mechanism showed that this chaotic system had Smale horseshoes (homoclinic chaos). Under satisfying the homoclinic Si' lnikov theorem, the large number of parameter values, which could be found, made that the system was chaotic state. Numerical simulation results show the effectiveness of the theoretical results. Finally, Smale horseshoses had been found in the system using undetermined-coefficient method, and it was chaotic in the sense of Si' lnikov. [ABSTRACT FROM AUTHOR]