We consider the hp-local discontinuous Galerkin finite element methods for nonlinear con-vection diffusion problems and use the novel method to deal with the nonlinear convection term. We obtain the hp-error estimates that are optimal in the mesh-size h and slightly suboptimal in the approximation degree. A numerical example is presented in the paper. The numerical results demonstrate that the LDG method is more accurate than the SIPG method (or NIPG method) and the LDG method is not sensitive to the penalty valueαfor large ps, but the SIPG method and the NIPG method are sensitive to the penalty valueαfor large ps.