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EDF-VD first focuses on the classic mixed-criticality task model in which all low criticality (LO) tasks are abandoned in the high criticality mode, which is an effective dynamic priority scheduling algorithm for mixed-criticality systems. However, it has low schedulability for the imprecise mixed-criticality (IMC) task model with constrained-deadlines, in which LO tasks are provided graceful degradation services instead of being abandoned. In this paper, we study how to improve schedulability for the IMC tasks model. First, we propose a novel criticality-aware EDF scheduling algorithm (CA-EDF) that tries to delay the LO task execution to improve schedulability. Second, we derive sufficient conditions of schedulability for CA-EDF based on the Demand Bound Function. Finally, we evaluate CA-EDF through extensive simulation. The experimental results indicate that CA-EDF can improve the schedulability ratio by about 13.10% compared to the existing algorithms.