This study proposes a collision-free motion planning framework for indoor autonomous flight of multirotor unmanned aerial vehicle (UAV) based on the convex model predictive control (MPC) approach under a three-dimensional point cloud environment. The suggested framework is divided into three steps: full reference path generation, piecewise flight corridor (PFC) creation, and MPC-based motion planning. The framework begins with reconstructing boundary surfaces that can encapsulate the given point cloud in order to generate a full reference path by applying Dijkstra and Voronoi diagram algorithms. Then PFC that represents locally convex and feasible flight corridor is generated using the current vehicle state, triangulized obstacle, and full reference path. In such a way, the entire problem breaks down into a series of discretized convex motion planning problems whose solution can be found by applying MPC iteratively until the UAV reaches its final destination. The constraints of the MPC are set up with the dynamics of the UAV, PFC, and the performance limitation of the platform. The framework is verified with simulation under a MATLAB environment. As a result, the UAV can find the control variable needed to reach the final destination with the suggested framework. Also, the computational time of the suggested framework is shorter than those of full reference path optimization methods.