In order to compute the constant-orientation workspace of serial robots, a fast search method based on the binary approximating principle is proposed. On the basis of binary tests of the inverse kinematics and the collision detection of a robot, this method introduces virtual straight lines containing the orientation information and selects two points (one locates inside the constant-orientation workspace, while the other outside) to carry out the dichotomy and test processes, so as to approach the boundary of the constant-orientation workspace step by step. Firstly, the concept and the state of the art of constant-orientation workspace are introduced in brief. The constant-orientation workspace problem is abstracted, followed by the basic solving ideas. Then the binary approximating search method and its applications to computing the 1D、2D and 3D constant-orientation workspace are presented in detail. Finally, the effectiveness of the proposed method is demonstrated by simulations and comparisons, showing that the method achieves the accuracy as 1mm consuming about 14.5ms to search the 1D constant-orientation workspace, and is suitable for solving the 1D ～ 3D collision-free constant-orientation workspace problem of robots with different degrees of freedom or configurations.