Quick UDP Internet Connection (QUIC) is a network transmission protocol proposed by Google which has lower latency, higher flexibility and stronger security compared with TCP. Multipath QUIC (MPQUIC) further enhance the user experience and adapt the large-scale network traffic by using multiple paths. Different from Multipath TCP (MPTCP), MPQUIC scheduler can perform finer granularity stream scheduling. In heterogeneous paths, MPQUIC not only has to consider inter-stream HoL blocking, but also encounters severe intra-stream HoL blocking within individual stream; in addition, MPQUIC scheduler needs to control scheduling rate to ensure that stream data is not backed up in sub-path queue, but also the bandwidth of sub-path is fully utilized. However, existing scheduling algorithms cannot solve the problems above. Therefore, we propose multi-stream hierarchical scheduling algorithm(MS-HS), which speeds up the transmission of high-priority streams by controlling data allocation rate and giving each stream two priority levels. We evaluate the benefits of MS-HS under heterogeneous paths by comparing it with the classical scheduler of MPQUIC. Our evaluation shows that our scheduler can reduce up to 31.4% of the high-priority stream completion time, while MS-HS achieves higher throughput than the original best scheduler.