Federated Learning (FL) is a promising privacy-preserving distributed learning framework where a server aggregates models updated by multiple devices without accessing their private datasets. Hierarchical FL (HFL), as a device-edge-cloud aggregation hierarchy, can enjoy both the cloud server's access to more datasets and the edge servers' efficient communications with devices. However, the learning latency increases with the HFL network scale due to the increasing number of edge servers and devices with limited local computation capability and communication bandwidth. To address this issue, in this paper, we introduce model pruning for HFL in wireless networks to reduce the neural network scale. We present the convergence rate of an upper on the $l_{2}$-norm of gradients for HFL with model pruning, analyze the computation and communication latency of the proposed model pruning scheme, and formulate an optimization problem to maximize the convergence rate under a given latency threshold by jointly optimizing the pruning ratio and wireless resource allocation. By decoupling the optimization problem and using Karush-Kuhn-Tucker (KKT) conditions, closed-form solutions of pruning ratio and wireless resource allocation are derived. Simulation results show that our proposed HFL with model pruning achieves similar learning accuracy compared with the HFL without model pruning and reduces about 50% communication cost.