A 140 GHz high power gyrotron with a gradually tapered cavity has been investigated and formed at the University of Electronic Science and Technology of China recently. After the study of cold cavities, a set of operating parameters of the optimized cavity is obtained as the TE29,8 mode is selected as the operating mode. The startup-scenarios of the potential competition modes have been investigated by simulation, which is based on a kind of quasi-self-consistent nonlinear theory for gyrotrons. After a lot of calculations, a better startup scenario is confirmed. Under the conditions that the beam voltage varies in 5 kV steps and the beam current and DC magnetic field are of 45 A and 5.64 T, respectively, the gyrotron with the operating mode TE29,8 brings out a theoretical power level of 1.2 MW at 140 GHz, corresponding to an overall efficiency of 35.5%. Meanwhile, the powers of parasitic modes are very low when the gyrotron operates at the proper parameters. At the same time, to study the limit state and its parameters of the designed gyrotron, further research has been carried out.