Dimensionless nonlinear dynamical equations of inclined support packaging system under the condition of dropping were established. Variational iteration method was proposed to solve the equation, expressions of approximate solution were obtained, and the results were compared with that of Runge-Kutta numeric method. The results showed that response frequency error of inclined support packaging system under the condition of dropping is less than 0.3%; the error of the max dimensionless displacement and the max dimensionless acceleration is less than 0.5%; and variation trend with dropping height and support angle is the same with Runge-Kutta numeric method. It was concluded that it is valid to apply variational iteration method to solve the problem of inclined support packaging system under the condition of dropping.