This paper extends the longitudinal walking controller of biped robots proposed by one of the authors to walking along a smooth curved path. The previous controller defined in a fixed inertial frame is redesigned with respect to a moving frame attached to the center of mass (COM) of the robot in order to achieve walking along an arc. As a result, it is found that a desired position of the zero-moment point (ZMP) can be determined only from the local curvature of the referential path besides the state of the robot with respect to the moving frame. Thus, it is directly applicable to walking along an arbitrary smooth path including straight walk. In addition to the extension of the ZMP manipulation, techniques of foot control consistent with COM movement and automatic update of the referential COM position are fully extended to curved walk. The idea was examined through computer simulations to show responsiveness to updates of motion references and robustness against external disturbances.