Galerkin coarse grid approximation (GCA) in multigrid methods is investigated for the incompressible Navier-Stokes equations in general coordinates. An efficient algorithm performing GCA is presented. The behavior of coarse grid matrices is studied under GCA with different transfer operators. For aquare and L-shaped driven cavaty problems, the performance of the multigrid methods using different combinations of transfer operators for the computation of coarse grid matrices and of coarse grid correction is investigated. Further computations are carried out in general coordinates for a channel flow problem with backward facing step in three dimensions.