A novel Smith-Purcell free-electron laser based on T-shaped grating is proposed herein. The influences of grating shape on the output characteristics of the Smith-Purcell free electron laser are discussed through theoretical analysis and Particle-in-Cell (PIC) simulation calculation. Through the theoretical analysis, it is found that the beam-wave interaction of the Smith-Purcell free electron laser based on the T-shaped grating and the bunching of electron beam are strong. Accordingly, the beam-wave conversion efficiency is strong, and the output power is high. Through the PIC simulation calculation, it is found that the Smith-Purcell free electron laser based on the T-shaped grating can increase the radiation power. Results indicate that a continuous-wave terahertz radiation at 0.753949 THz with a peak output power of approximately 2 kW can be obtained for a grating of period D=0.3 mm operating at a beam energy of E=50 keV and beam current i=10 A in this novel device. However, in the Smith-Purcell free electron laser based on rectangular grating, continuous-wave terahertz radiation at 0.723397 THz with a peak output power of approximately 0.3 kW can only be generated by the same electron beam (energy E=50 keV and beam current i=10 A) passing through the grating with the same size (D=0.3 mm).