In the paper, an inf-sup stabilized finite element method by multiscale
functions for the Stokes equations is discussed. The key idea is to use a Petrov-Galerkin approach based on the enrichment of the standard polynomial space for
the velocity component with multiscale functions. The inf-sup condition for $P_1$-$P_0$ triangular element (or $Q_1$-$P_0$ quadrilateral element) is established. And the optimal
error estimates of the stabilized finite element method for the Stokes equations
are obtained.