In the last decade, the rapid evolution of the Commercial-Off-The-Shelf (COTS) platforms led safety-critical systems towards integrating tasks and applications with different criticality levels in a shared hardware platform, i.e., Mixed-Criticality Systems (MCS)s. Therefore, several scheduling algorithms and approaches have been proposed upon a commonly used model, i.e., Vestal's model. However, consolidating software functions onto shared processors cannot be implemented directly in real-life applications and industrial systems while complying with certification requirements. The existing scheduling approaches do not provide a simple solution for eliminating the interference effect among the tasks with different criticality levels on the shared processing resources. Moreover, the system mode switch guarantees the timing constraints of the high-criticality tasks throw the termination of the low-criticality tasks. In this paper, we developed a new scheduling algorithm that addresses these challenges based on the round-robin technique, which improves the overall schedulability. We compared the proposed algorithm against existing scheduling algorithms in both academia and industry using extensive experiments to evaluate it. Our results show improvements in the schedulability from 0.8% to 14.0% and from 2.7% to 10.7% compared to the conventional Earliest Deadline First with Virtual Deadline (EDF-VD) and Fixed Priority Preemptive (FPP) scheduling approaches, respectively.