The increasing interest in high-order discretization techniques for CFD applications is motivated by the high accuracy that these methods provide compared to low-order methods. In this project, the hybridizable discontinuous Galerkin (HDG) method is discussed. HDG represents a novel and competitive alternative to the classical discontinuous Galerkin method by substantially reducing the number of coupled unknowns of the discrete problem. Some numerical examples for the simulation of steady incompressible flows are presented, with special emphasis on the HDG stabilization term in order to ensure the optimal convergence of velocity, pressure and gradient of velocity and the superconvergence of a postprocessed velocity field.