Both resource access protocols and real-time scheduling algorithms have been extensively studied in classic embedded real-time systems. However, there has been relatively little attention given to the resource access protocol and real-time scheduling algorithms in mixed-criticality systems. In this article, we pay attention to the problem of scheduling an imprecise mixed-criticality (IMC) taskset on a multiprocessor platform with shared resources. First, we propose an IMC with MSRP (IMC-MSRP) resource access protocol, which ensures mutually exclusive access to the shared resources for the tasks. Second, we propose the schedulability test based on the IMC-multiprocessor stack resource policy (MSRP) for a given task-to-processor mapping method. Third, we propose a feasible task-to-processor mapping algorithm called resource-aware criticality-unaware worst-fit decreasing (RA-CU-WFD), which first assigns tasks sharing the same resources to the same processor to reduce the global waiting time of the tasks and thus improve the schedulability ratio of the system. And then assigns tasks based on the criticality-unaware worst-fit decreasing (CU-WFD) algorithm. Finally, we conduct experiments using the synthetic tasksets, and the experimental results show that the RA-CU-WFD outperforms the other approaches in terms of the schedulability ratio.