In this talk, an isogeometric discontinuous Galerkin finite element method for 2D Euler equations is proposed. The idea of isogeometric is integrated into the discontinuous Galerkin framework to solve compressible flow problems by the knots insertion and degree elevation techniques in NURBS (Non-Uniform Rational B-Splines). Since the computational grids are inherently defined by the knot vectors of the NURBS parameterization of the physical domain, not only the mesh generation procedure is greatly simplified, but also the curved boundaries as well as the interfaces between neighboring elements are naturally and exactly resolved. The formulations of this method for solving 2D Euler equations are presented. Several typical test cases are selected to demonstrate its accuracy, stability and flexibility in handling curved geometry.