The generalized Gaussian principle and dynamic equation of relative motion with variable acceleration are studied. Firstly, the equation of force change rate is obtained by derivation of the kinetic equation of relative motion of particle, and the concept of space of relative jerky is put forward and the generalized Gaussian principle of relative motion with variable acceleration is constructed in this space. Secondly, the generalized compulsion function of variable acceleration relative motion is defined, and it is proved that the real motion minimizes it. The Appell, Lagrange and Nielsen forms of the generalized Gaussian principle of relative motion with variable acceleration under generalized coordinates are derived by introducing the acceleration energy and the jerky energy of relative motion. Finally, the dynamics equations of the relative motion of holonomic and nonholonomic systems with variable acceleration are derived from the obtained principles.