Gauss′s minimum constraint principle is a typical differential variation principle, where the acceleration is the variable, and the motion law of the system can be obtained directly by the variation method of seeking the extreme of the constraint function. At present, Lagrange multiplier method is widely used for solving the Gauss constraint function. Through the introduction of Lagrange multipliers, the conditional extreme value problem of Gauss constraint function is transformed to the unconditional extreme problem. However, this method increase the number of unknown variables. In order to reduce the number of variables, it need further study to improve the operation efficiency. In this paper, the deformation on Gauss constraint function is firstly simplified. The constraint equations of the acceleration form are also introduced into the Gauss constraint equations to get the least square form of equations. The least square method is then used to export the expression of the true acceleration of the system, which can make the Gauss binding function to take the minimum value. In the end, the validity of the method is verified by analyzing and calculating the normal dynamics of the crank slider mechanism.