This paper analyzes the asymptotic problem of a kinked crack in an anisotropic material under antiplane deformation. Using the linear transformation method proposed in this paper, a solution to the asymptotic problem of a kinked crack in an anisotropic material can be obtained from the solution of the corresponding isotropic kinked crack problem. The exact solution of the stress intensity factor for the kinked crack in the anisotropic material is obtained from the solution of the isotropic problem. The effect of the kink angle and two anisotropic parameters on the stress intensity factor is discussed for the inclined orthotropic material as well as the anisotropic material. In order to verify the exact solution of the stress intensity factor, numerical calculations are performed by using finite element analysis.