Abstract: An algorithm for 1D and 2D Euler equations was proposedby combining the Roe scheme and the semi-Lagrangian method based oncharacteristic theory. The finite volume method (FVM) is cast in a flux formand thus guarantees the numerical conservation. We calculated the flux atthe cell boundary by using its value at the boundary's center, which couldmake the algorithm second-order accuracy in time. The semi-Lagrangian methodwith characteristic theory was implemented to trace the fluid particles. Thecharacteristic velocities were modified based on Roe average to locate thedeparture points. The interpolation by ENO reconstruction made the algorithmfree of limiters. The high order algorithm is simple and convenient toimplement. The numerical results showed that it was competitive comparingwith other schemes.