A projective multigrid method is considered for application to fermion propagators in the presence of gauge fields. The collective variables on each block are defined by the gauge-invariant projection onto the lowest eigenstate for the block. The scheme is formulated in detail for two-dimensional bosons and Wilson fermions in the U(1) gauge theory and numerical studies are presented for bosons to demonstrate its potential for more efficient convergence. For example, at a confinement length of 8 lattice units on a 64 x 64 lattice, the projective multigrid method gives a speed up of almost two orders of magnitude relative to the Gauss-Seidel algorithm.