We introduce the technique of perturbation of boundary condition to the problem of terahertz two-wire metallic waveguides with different radii. Based on the quasi-TEM analytical mode fields derived by use of Möbius transformation, a concise expression for the complex effective index is obtained analytically. The expression is in good agreement with the simulation result. Further, the dispersion and attenuation are obtained from the expression. In addition, we find a zero value point of the group velocity dispersion around 1.268 THz. The results show that the technique of perturbation of boundary condition is helpful in the analysis and design of terahertz metal waveguide.