Using the approach based on conformal symmetry we calculate the three-loop (NNLO) contribution to the evolution equation for flavor-nonsinglet leading twist operators in the (MS) over bar scheme. The explicit expression for the three-loop kernel is derived for the corresponding light-ray operator in coordinate space. The expansion in local operators is performed and explicit results are given for the matrix of the anomalous dimensions for the operators up to seven covariant derivatives. The results are directly applicable to the renormalization of the pion light-cone distribution amplitude and flavor-nonsinglet generalized parton distributions.