As real-time embedded systems are required to accommodate various tasks with different levels of criticality, scheduling algorithms for MC (Mixed-Criticality) systems have been widely studied in the real-time systems community. Most studies have focused on MC uniprocessor systems whereas there have been only a few studies to support MC multiprocessor systems. In particular, although the ZL (Zero-Laxity) policy has been known to an effective technique in improving the schedulability performance of base scheduling algorithms on SC (Single-Criticality) multiprocessor systems, the effectiveness of the ZL policy on MC multiprocessor systems has not been revealed to date. In this paper, we focus on realizing the potential of the ZL policy for MC multiprocessor systems, which is the first attempt. To this end, we design the ZL policy for MC multiprocessor systems, and apply the policy to EDF (Earliest Deadline First), yielding EDZL (Earliest Deadline first until Zero-Laxity) tailored for MC multiprocessor systems. Then, we develop a schedulability analysis for EDZL (as well as its base algorithm EDF) to support its timing guarantee. Our simulation results show a significant schedulability improvement of EDZL over EDF, demonstrating the effectiveness of the ZL policy for MC multiprocessor systems.