High-repetition-rate target injection and precise steering of multiple laser beams are essential for realizing laser-driven inertial fusion energy (IFE) reactors. EX-Fusion Inc. has established a facility to demonstrate these capabilities for the Fast Ignition scheme named the EX-Fusion Continuous Operation Laser Reactor (XF-COLR). Laser beam tracking and illumination of a free-falling stainless steel ball with a diameter of 1 mm were carried out at 10 Hz using multiple nanosecond and femtosecond lasers. The system with real-time correction of beam positions continuously operated for up to 12 h under ambient conditions and for 2.5–3 min under vacuum. Tracking performance, evaluated as standard deviations for 1500 shots under vacuum conditions, reached 121–139 m in the horizontal direction and 63–121 m in the vertical direction. The expected uncertainty at the engagement point propagated from the sensors was approximately 157 m. To the best of our knowledge, this is the first demonstration of dynamic tracking of an injected target using multiple laser beams steered by mirrors at 10 Hz, providing a reference for the development of future IFE reactors.