Unmanned Aerial Vehicles (UAVs) act-ing as aerial users to access the cellular network form a promising solution to guarantee its safe and effi-cient operations via the high-quality communication. Due to the flexible mobility of UAVs and the coverage range limits of ground base station(GBS), the signal-to-noise ratio (SNR) of the communication link be-tween UAVs and GBS will fluctuate. It is an important requirement to maintain the UAV's cellular connection to meet a certain SNR requirement during the mission for UAV flying from take off to landing. In this pa-per, we study an efficient trajectory planning method that can minimize a cellular-connected UAV's mission completion time under the connectivity requirement. The conventional method to tackle this problem adopts graph theory or a dynamic programming method to optimize the trajectory, which generally incurs high computational complexities. Moreover, there is a non-negligible performance gap compared to the optimal solution. To this end, we propose an iterative trajec-tory optimizing algorithm based on geometric plan-ning. Firstly, we apply graph theory to obtain all the possible UAV-GBS association sequences and se-lect the candidate association sequences based on the topological relationship among UAV and GBSs. Next, adopting the triangle inequality property, an iterative handover location design is proposed to determine the shortest flight trajectory with fast convergence and low computation complexity. Then, the best flight trajec-tory can be obtained by comparing all the candidate trajectories. Lastly, we revealed the tradeoff between mission completion time and flight energy consump-tion. Numerical results validate that our proposed so-lution can obtain the effectiveness with set accuracy and outperform against the benchmark schemes with affordable computation time.