This paper investigates the challenging problem of the autonomous landing of a quadrotor on a moving platform in a non-cooperative environment. The limited sensing ability of quadrotors often hampers their utilization for autonomous landing, especially in GPS-denied areas. The performance of motion capture systems (MCSs) in many application areas is the motivation to utilize them for the autonomous take-off and landing of the quadrotor in this research. An autonomous closed-loop vision-based navigation, tracking, and control system is proposed for quadrotors to perform landing based upon Model Predictive Control (MPC) by utilizing multi-objective functions. The entire process is posed as a constrained tracking problem to minimize energy consumption and ensure smooth maneuvers. The proposed approach is fully autonomous from take-off to landing; whereas, the movements of the landing platform are pre-defined but still unknown to the quadrotor. The landing performance of the quadrotor is tested and evaluated for three different movement patterns: static, square-shaped, and circular-shaped. Through experimental results, the pose error between the quadrotor and the platform is measured and found to be less than 30 cm.