Task scheduling is one of the major issues to achieve high performance in distributed systems such as Grid, Peer-to-Peer and cloud environment. Generally, there are two phases in heuristics-based task scheduling algorithms in heterogeneous distributed computing systems (HeDCSs). These phases are task prioritization and processor assigning respectively. Heuristic-based task scheduling algorithms may use different policies to assign priority to subtasks which produce different makespans in a heterogeneous computing system. Thus, a suitable scheduling algorithm is one that can efficiently assign a priority to tasks in order to minimize makespan. Recently, memetic algorithms (MAs) have been used as evolutionary or population-based global search approaches with local search heuristic to optimize NP-complete problems. Recent studies on MAs have discovered their success on a wide variety of real-world problems. Since the task scheduling problem is an NP-complete, in this paper, a new task scheduling algorithm on cloud environment using multiple priority queues and a memetic algorithm (MPQMA) is proposed. The proposed method uses a genetic algorithm (GA) along with hill climbing to assign a priority to each subtask while using a heuristic-based earliest finish time (EFT) approach to search for a solution for the task-to-processor mapping. The basic idea of our approach is using the advantage of MA to increase the convergence speed of the solutions. We implemented the algorithm on Azure Cloud Service by C# language where the experimental results for the set of randomly generated graphs revealed that the proposed MPQMA algorithm outperformed the existing three task scheduling algorithms in terms of makespan with fast convergence to the optimized solution.