Summary: A Galerkin finite element discretization of a convection-diffusion boundary value problem is considered on two special types of layer-fitted meshes: Shishkin and Gartland-type meshes. The interpolation and discretization error is estimated for two typical problems with exponential and parabolic boundary layers, respectively. For the Galerkin method we obtain uniform convergence (with respect to the perturbation parameter \(\varepsilon\)) in the \(\varepsilon\)-weighted \(H_1\) norm. As well as the previously known result of order \(O(H\ln(1/H))\) for Shishkin meshes applied to exponential layers, we show that the order of convergence is of order \(O(H)\) in all the other cases considered, where \(H\) denotes the mesh diameter. Numerical experiments show that the Galerkin finite element method sometimes yields significantly better accuracy on Gartland-type meshes than on Shishkin meshes.