In this paper a Lie point symmetry- preserving difference schemes approximating holonomic constrained mechanical systems is presented. The procedure is as follows: Firstly we find the Lie point symmetry groups of the original equation, and prolong them to three points of the lattice. Secondly the discrete invariants are obtained by solving discrete characteristic equations, then the invariant difference scheme is constructed by using these discrete invariants; and this invariants difference scheme will give the original equation under the continuous limit. Finally an example is presented to illustrate the applications of the result.