A variant of the preconditioned conjugate gradient method to solve generalized least squares problems is presented. If the problem is min ( Ax − b) T W −1( Ax − b) with A ∈ R m× n and W ∈ R m× m symmetric and positive definite, the method needs only a preconditioner A 1 ∈ R n× n , but not the inverse of matrix W or of any of its submatrices. Freund's comparison result for regular least squares problems is extended to generalized least squares problems. An error bound is also given.