A modified Smith-Purcell free-electron-laser based on two tandem cylindrical-gratings is proposed. The preset grating with larger size, operating in the slow-wave condition, is to prebunch the initial continuous electron-beam, and the postpositive grating with smaller size, operating in the fast-wave condition, is used as the main radiator. Compared with traditional Smith-Purcell free-electron-lasers operating at the second harmonic of the bunched-beam, the present scheme operates at much higher harmonics, fifth and sixth harmonics have been achieved, and the radiation frequency is greatly increased consequently. And also the radiation power is enhanced by tens of times. Thus it could be developed as an efficient terahertz source with frequency being over 0.5 THz in practice.