A stochastic model of business cycle was presented in this paper. The Ito diffusion process was obtained after the model was simplified in quasi Hamiltonian theory. The backward Kolmogorov equation for reliability function and the generalized Pontryagin equation for conditional moment of the first-passage time were established, and the numerical results were given in virtue of figures according to the classification of boundary conditions and initial conditions of the two equations. Finally, the influence of parameters on the first-passage problem was analyzed.