The present invention discloses a chaotic forecasting method of an asymmetric piecewise continuous nonlinear constraint system, relating to the technical field of vibration behavior forecasting of dynamic systems under piecewise nonlinear constraints. By adopting the method, the problem of judging chaotic motion states of vibration systems under piecewise nonlinear constraint effects can be solved. The method comprises the following steps: determining a dynamic model of the asymmetric piecewise continuous nonlinear constraint system according to a general formula of an asymmetric piecewise continuous nonlinear constraint model and the dynamic model; determining a homoclinic orbit parameter equation of a saddle point by analyzing the saddle point of the asymmetric piecewise continuous nonlinear constraint system according to the dynamic model; determining a Melnikov function of the asymmetric piecewise continuous nonlinear constraint system according to a general formula of the dynamic model and the Melnikov function; determining upper and lower limits of integrals of the Melnikov function according to the asymmetric piecewise continuous nonlinear constraint model and the homoclinic orbit parameter equation; and determining critical conditions of the asymmetric piecewise continuous nonlinear constraint system in a chaotic motion process according to the Melnikov function and the upper and lower limits of integrals.