In this paper, the design studies of a triple frequency (170/204/236GHz) coaxial cavity gyrotron are carried out which is suitable for plasma heating application in a commercial fusion demonstration (DEMO) tokamak class prototype reactor. To reduce the spatial and maintenance requirements in the heating system of the DEMO tokamak, the output power of the proposed gyrotron is targeted at ≈3 MW for all the three operating frequencies. The cavity modes are selected by considering various physical and technical constraints of the multifrequency gyrotron. The dimensions of the interaction cavity are optimized for the chosen modes at the desired frequencies through cold-cavity calculations. Mode competition studies are then performed to understand the effect of the parasitic modes on the desired modes around the operating frequencies. A triangular corrugated coaxial insert is considered for reducing the problem of localized heating. Initial optimization of beam parameters and magnetic field is carried out using single-mode calculations for the maximum output efficiency. A triode-type coaxial magnetron injection gun is designed for support ... mehring this multifrequency operation. Startup calculations are carried out with beam space-charge neutralization at all the three operating frequencies. These studies predict that a 3-MW, continuous-wave operation is possible at the desired frequencies of the proposed DEMO class gyrotron.