In this paper, a trapezoidal periodically poled magnesium doped lithium niobate (PPMgLN) waveguide was designed, and its acceptable bandwidth of the pump source during frequency doubling (SHG) process can be widened by introducing a temperature gradient along the propagation direction. The effective refractive index of the waveguide was calculated and the dimension of the waveguide was designed by the finite difference beam propagation method. The results show that, by changing the temperature at different positions of the trapezoidal waveguide to form a temperature gradient, the wavelength receiving bandwidth of the pump light source can be widened. The maximum receiving bandwidth of the PPMgLN waveguide pump light source designed in this paper is C-band, which range is from 1 530 nm to 1 565 nm. The waveguide can double the frequency of C-band, and the output band bandwidth is 765 nm to 782.5 nm, and the temperature tuning range is from 30 ℃ to 150 ℃.