This study focused on acceleration of propellant to supersonic speed with a compact engine. Increase in the exhaust velocity of a rocket engine leads to improvement of the thrust performance. Several combustion tests were conducted for a small rotating detonation engine (RDE) whose channel is truncated conical shaped (diverging angle (formula presented)), under low back pressure conditions. In these tests, gaseous (formula presented) were used as the propellant, and the mass flow rate were ranged from 56 to 123 g/s. The pressure ratio between the maximum value in the engine and at the exit was approximately 0.16, which was confirmed to be significantly below the critical value for a sonic flow. Namely, the exhaust flow was supersonic, even though there was no convent section in the engine. In a range of propellant mass flow rate, specific impulses were approximately 110% compared to those in a cylindrical RDE with a uniform cross-section combustor.