Abstract: A high-order discontinuous method (DGM) is integrated with adaptive method to solve Euler equations on unstructured mesh. Contribution of the polynomial's highest-order terms is quantified in the form of artificial viscous coefficient. The coefficient is regarded as the indicator of h-adaptivity. Elements where the coefficients are greater than the upper limit are refined. Those where the coefficients are less than the lower limit are coarsened if they have been refined. A high-order geometric approximation of curved boundaries is adopted to ensure the convergence. Numerical results of test cases are consistent with corresponding experimental ones. High accurate numerical results can be obtained with the h-adaptive method at low expense.