In this paper, we propose a new hybridized discontinuous Galerkin (DG) method for the convection-diffusion problems with mixed boundary conditions. A feature of the proposed method, is that it can greatly reduce the number of globally-coupled degrees of freedom, compared with the classical DG methods. The coercivity of a convective part is achieved by adding an upwinding term. We give error estimates of optimal order in the piecewise H-1-norm for general convection-diffusion problems. Furthermore, we prove that the approximate solution given by our scheme is close to the solution of the purely convective problem when the viscosity coefficient is small. Several numerical results are presented to verify the validity of our method.