Network signal control is an effective way to mitigate traffic congestion. However, most network signal control methods ignore the risk of queue spillback. Although local and decentralized control methods have the potential to address spillback, their performance at the system/network level is not guaranteed, making it challenging to achieve the global optimum. This study proposes a novel hierarchical model predictive control (MPC) approach that utilizes the link transmission model (LTM) with queue transmission at both road segment and turn levels to optimize traffic signals for road networks. At the network level, the controller employs a state-of-the-art LTM framework that can describe segment-level flow dynamics and uses quadratic programming to determine the effective fractions of green time for network throughput maximization. The network decisions of green time fractions are sent to the local layer as a reference. The local layer builds on a refined LTM with turn-level queue transmission and formulates a nonlinear programming problem to track the reference to ensure that the optimal network decision is realized at the individual intersections while eliminating potential spillback. Simulation experiments on both an arterial and a grid network are conducted to verify the performance of the proposed approach. The results reveal that the proposed MPC leads to substantial improvements in terms of throughput and queue length, especially in oversaturated conditions, and is robust against demand prediction errors.