The total chromatic number χT (G) of a graph G is the minimum number of colors needed to color the edges and the vertices of G so that incident or adjacent elements have distinct colors. We show that if G is a regular graph and d(G) 2 3 |V (G)| + 23 6 , where d(G) denotes the degree of a vertex in G, then χT (G) d(G) + 2.