In autonomous driving, an unprotected left turn is a highly challenging scenario. It refers to the situation where there is no dedicated traffic signal controlling the left turns; instead, left-turning vehicles rely on the same traffic signal as the through traffic. This presents a significant challenge, as left-turning vehicles may encounter oncoming traffic with high speeds and pedestrians crossing against red lights. To address this issue, we propose a Model Predictive Control (MPC) framework to predict high-quality future trajectories. In particular, we have adopted the infinity norm to describe the obstacle avoidance for rectangular vehicles. The high degree of non-convexity due to coupling terms in our model makes its optimization challenging. Our way to solve it is to employ Sequential Convex Optimization (SCP) to approximate the original non-convex problem near certain initial solutions. Our method performs well in the comparison with the widely used sampling-based planning methods.