Network-on-chip (NoC) has emerged as a vital factor that determines the performance and power consumption of many-core systems. This paper proposes a hybrid scheme for NoCs, which aims at obtaining low latency and low power consumption. In the presented hybrid scheme, a novel switching mechanism, called virtual circuit switching, is proposed to intermingle with circuit switching and packet switching. Flits traveling in virtual circuit switching can traverse the router with only one stage. In addition, multiple virtual circuit-switched (VCS) connections are allowed to share a common physical channel. Moreover, a path allocation algorithm is proposed in this paper to determine VCS connections and circuit-switched connections on a mesh-connected NoC, such that both communication latency and power are optimized. A set of synthetic and real traffic workloads are exploited to evaluate the effectiveness of the proposed hybrid scheme. The experimental results show that our proposed hybrid scheme can efficiently reduce the communication latency and power. For instance, for real traffic workloads, an average of 20.3% latency reduction and 33.2% power saving can be obtained when compared with the baseline NoC. Moreover, when compared with the NoC with virtual point-to-point connections (VIP), the proposed hybrid scheme can reduce the latency by 6.8% with the power decreasing by 11.3% averagely.