Despite tremendous efforts made for years, trajectory tracking control (TC) of a nonholonomic mobile robot (NMR) without global positioning system remains an open problem. The major reason is the difficulty to localize the robot by using its onboard sensors only. In this paper, a newly designed adaptive trajectory TC method is proposed for the NMR without its position, orientation, and velocity measurements. The controller is designed on the basis of a novel algorithm to estimate position and velocity of the robot online from visual feedback of an omnidirectional camera. It is theoretically proved that the proposed algorithm yields the TC errors to asymptotically converge to zero. Real-world experiments are conducted on a wheeled NMR to validate the feasibility of the control system.