Complex chaotic dynamics is studied in the van tier Pol oscillator model of business cycle forced by a sinusoidal function.The famous topological horseshoe theorem is applied to prove the existence of chaos from the mathematical viewpoint in this business cycle model.A rigorous proof for the existence of topological horseshoe is given.This technique combines the topological theory, with the computer-assisted computations.A proper Poincaré section is first chosen to obtain the corresponding Poincaré map, which is proved to be semi-conjugate to the 2-shift map.This result implies that the business cycle model has positive topological entropy, and thus is definitely chaotic.