Abstract: Motion equations of multibody systems with holonomic constraints via the first kind of Lagrange's equations are index-3 differential-algebraic equations (DAEs).As for the velocity-constrained equations are considered,over-determined motion equations can be obtained and named as index-2 over-determined differential-algebraic equations (ODAEs).Generalized-α method,which is used in the structural dynamics simulation,is extended to the numerical integration of motion equations in the form of index-2 ODAEs.For the new generalized-α method,the number of nonlinear equations from discretization is not increased compared with other integration methods for the index-2 ODAEs.The new method is validated by numerical experiments.There are no accuracy reductions for the new method in the integration of index-2 ODAEs and it is second-order accuracy.In addition,the numerical dissipation is controllable.In the end,new generalized-α method for motion equations in the form of ODAEs is compared with other methods from the point view of the CPU time.