This paper proposes a quasi-passive dynamic autonomous control (Q-PDAC) for a three-dimensional (3-D) bipedal gait of humanoid robots from start points to goal points. The major approach for 3-D traveling is currently footstep planning by a constantly stable gait with an emphasis on its accurate and secure traveling. However, energy would potentially be wasted when the robot accurately travels according to the planned footsteps. In contrast, a limit-cycle-based gait possesses the good efficiency by a gait speed control, although the accurate and secure traveling is difficult for it. Its gait speed control is unfortunately not enough to freely travel on 3-D spaces: shortages of a turning speed control, trackability of horizontal speed, and stability of the bipedal gait. Hence, the Q-PDAC supplies three proper angular momenta by hip and ankle joints to achieve the turning motion and enhance the trackability of horizontal motion. Three angular momenta are simply designed consistent in the PDAC dynamics, and achieved the sufficient gait speed control for 3-D traveling. As a result, the robot can efficiently travel from the start point to the goal point while following a leader point not to collide with walls.