An adjoint variable method was established for sensitivity analysis of multibody system dynamics described by differential/algebraic equations based on general objective function, which had high efficiency for systems with many design parameters and avoided the complex derivatives computation of the generalized coordinates with respect to design parameters. The adjoint variable equations for the first order sensitivity analysis and design sensitivity formulations were derived, and the detailed processes of the design sensitivity algorithm were presented. For the purpose of simplification, the objective function and its first derivative were transformed into an initial value problem of ordinary differential equation with one variable. An example of slidecrank system was given to validate the method presented.