One of control methods used in underactuated manipulators is known as a switching control, which selects a partially-stable controller with a prespecified switching rule. A switching computed torque control integrated with a fuzzy-energy regions method has been proposed, and applied to control a two degrees-of-freedom (dofs) underactuated manipulator with one active degree-of-freedom (dof) and one passive dof. The energy space used to design the switching rules was a two-dimensional space. However, it is difficult to design a controller for underactuated systems with more than two-dofs. In this paper, we propose a switching rule for three-dofs underactuated manipulator with suitable mapping to reduce the dimension of energy space. The effectiveness of the proposed method is illustrated through simulations with a three-dofs underactuated manipulator.