In the two-dimensional convection-diffusion finite-element analysis, various kinds of elements are adopted for practical uses, such as a triangular element and a rectangular element. However, there seems to be no research on the computational error estimation of these various kinds of elements. In this paper, we estimate the numerical error for four different triangular elements and a rectangular element using the error analysis technique. The Galerkin Method (GL) and our previously proposed modified Galerkin Method (MGM) were investigated at the same time. From the error analysis results, we found that MGM offered greater effectiveness than GL and higher accuracy of a rectangular element or a regular triangular element than other triangular elements. Through numerical experiments using these five different elements, we confirmed the general correspondence between the error analysis results and the numerical simulation ones.