Autonomous landing on a moving target is challenging because of external disturbances and localization errors. In this paper, we present a vision-based guidance technique with a log polynomial closing velocity controller to achieve faster and more accurate landing as compared to that of the traditional vertical landing approaches. The vision system uses a combination of color segmentation and AprilTags to detect the landing pad. No prior information about the landing target is needed. The guidance is based on pure pursuit guidance law. The convergence of the closing velocity controller is shown, and we test the efficacy of the proposed approach through simulations and field experiments. The landing target during the field experiments was manually dragged with a maximum speed of $0.6$ m/s. In the simulations, the maximum target speed of the ground vehicle was 3 m/s. We conducted a total of 27 field experiment runs for landing on a moving target and achieved a successful landing in 22 cases. The maximum error magnitude for successful landing was recorded to be 35 cm from the landing target center. For the failure cases, the maximum distance of vehicle landing position from target boundary was 60 cm.