The strategies and approaches of designing chirped Distributed Bragg Reflector for group velocity compensation in metal-metal waveguide terahertz quantum cascade laser are investigated through 1D and 3D models. The results show the depth of the corrugation periods plays an important role on achieving broad-band group velocity compensation in terahertz range. However, the deep corrugation also brings distortion to the group delay behavior. A two-section chirped DBR is proposed to provide smoother group delay compensation while still maintain the broad frequency range (octave) operation within 2 THz to 4 THz.