In this paper, we address the design of a navigation control algorithm for the autonomous landing of a quadrotor on a moving mobile platform. The quadrotor's velocity is unknown, and we assume that it is equipped with an on-board downward-looking single camera for determining its position relative to the target. The proposed autonomous landing operation proceeds in three phases: the search phase, the homing phase, and the landing phase. To prepare for these phases, a safety sphere with a desired radius having the target position as its center is constructed along with a virtual target point that can move on its surface. During the docking procedure, the quadrotor is first commanded to reach the virtual target point; as it approaches this target point, a second stage is initiated to provide the quadrotor with more precise guidance to land safely on the mobile platform. The core design of the landing algorithm is proposed based on a concise adaptive tracking control scheme using backstepping and dynamic surface control. Simulations are carried out to validate the effectiveness of the proposed guidance landing control approach.