MotiVated by recent experimental realization of synthetic spin-orbit coupling in neutral quantum gases, we consider the quasi-two-dimensional rotating two-component Bose-Einstein condensates with anisotropic Rashba spin-orbit cou- pling subject to concentrically coupled annular potential. For experimentally feasible parameters, the rotating condensate exhibits a variety of rich ground state structures by varying the strengths of the spin-orbit coupling and rotational frequency. Moreover, the phase transitions between different ground state phases induced by the anisotropic spin-orbit coupling are obviously different from the isotropic one.
