In this article, we propose an adaptive grid based on mesh equidistribution principle for two-parameter convection-diffusion boundary value problems with continuous and discontinuous data. A numerical algorithm based on an upwind finite difference operator and an appropriate adaptive grid is constructed. Truncation errors are derived for both continuous and discontinuous problems. Parameter uniform error bounds for the discrete solution are established. Numerical examples are carried out to show the performance of the proposed method on the adaptive grids.