Scheduling of coflows, each a collection of parallel flows sharing the same objective, is an important task of data transmission that arises in the networks supporting data-intensive applications such as data center networks (DCNs). The hybrid switch design combining the optical circuit switch (OCS) and electrical packet switch (EPS) for transmitting high-volume and low-volume traffic separately has received considerable research attention. To support this design, efficient scheduling of coflows on hybrid network links is crucial for reducing the overall communication time. However, because it needs to consider both reconfiguration delay of circuit switching in the OCS and bandwidth limitation of packet switching in the EPS, coflow scheduling on hybrid network links is more challenging than on monotonic network links of either OCS or EPS. The existing coflow scheduling algorithms in hybrid switches are all heuristic and provide no performance guarantees. In this work, we first propose an approximation algorithm with a worst-case performance guarantee of $2\tau$ , where $\tau \le N$ is the maximum number of non-zero elements of each row and column of coflow’s demand matrix, for single coflow scheduling in an $N\times N$ hybrid switch to minimize the coflow completion time (CCT). We then extend the algorithm for scheduling multiple coflows to minimize the total weighted CCT with a provable performance guarantee of $\mu \tau _{\max }$ , where $\mu =4M\cdot \frac {w_{\max }}{w_{\min }}$ , $\tau _{\max }=\max _{1\le m\le M}\tau _{m}\leq N$ , $w_{\max }$ and $w_{\min }$ are respectively the maximum and minimum weights of the $M$ coflows. Extensive simulations using Facebook data traces show that our algorithms outperform the state-of-the-art coflow scheduling schemes. Specifically, our algorithms transmit a single coflow up to $1.08\times$ faster than Solstice (hybrid switch) and $1.42\times$ faster than Reco-Sin (pure OCS), and multiple coflows up to...