With the rapid advancement of technology, parallel computing applications have become increasingly popular and are commonly executed in large data centers. These applications involve two phases: computation and communication, which are executed repeatedly to complete the work. However, due to the ever-increasing demand for computing power, large data centers are struggling to meet the massive communication demands. To address this problem, coflow has been proposed as a networking abstraction that captures communication patterns in data-parallel computing frameworks. This paper focuses on the coflow scheduling problem in identical parallel networks, where the primary objective is to minimize the makespan, which is the maximum completion time of coflows. It is considered one of the most significant $\mathcal{NP}$-hard problems in large data centers. In this paper, we consider two problems: flow-level scheduling and coflow-level scheduling. In the flow-level scheduling problem, distinct flows can be transferred through different network cores, whereas in the coflow-level scheduling problem, all flows must be transferred through the same network core. To address the flow-level scheduling problem, this paper proposes two algorithms: a $(3-\tfrac{2}{m})$-approximation algorithm and a $(\tfrac{8}{3}-\tfrac{2}{3m})$-approximation algorithm, where $m$ represents the number of network cores. For the coflow-level scheduling problem, this paper proposes a $(2m)$-approximation algorithm. Finally, we conduct simulations on our proposed algorithm and Weaver's algorithm, as presented in Huang \textit{et al.} (2020) in the 2020 IEEE International Parallel and Distributed Processing Symposium (IPDPS). We also validate the effectiveness of the proposed algorithms on heterogeneous parallel networks.