Time-sensitive networking (TSN) is an emerging technology widely used in real-time systems for its high bandwidth and deterministic timing properties. To ensure the deterministic transmission of Time-triggered (TT) messages, a guard band mechanism is employed to prevent interference from other messages, such as Audio-Video Bridging (AVB) and Best-effort (BE) messages, before transmitting the TT messages in TSN. However, this mechanism introduces transmission delays for non-TT messages and bandwidth wastes for the physical links. Another challenge arises from the default First-in-first-out (FIFO) order of incoming messages, resulting in a relatively low acceptance rate for non-TT messages. To address these issues, a hybrid scheduling algorithm based on the min-heap structure (HSMH) is proposed. For AVB messages, HSMH sorts them in ascending style on the basis of deadlines, guaranteeing the earliest deadline message to be sent first. For BE messages, a threshold is designed to diverge them into two queues: a FIFO queue and a STF (shortest-time-first) queue. The former outputs the messages in a FIFO style, while the latter outputs messages in a STF style. All the output order of AVB messages and STF-queue messages are arranged in a min-heap structure. The algorithm can efficiently improve the transmission rate of AVB messages, the sending rate of BE messages, and the overall link utilization. Experimental results demonstrate that the proposed algorithm outperforms existing approaches in all these three aspects.