Resource allocation (RA) is a significant aspect of Cloud Computing. The Cloud resource manager is responsible to assign available resources to the tasks for execution in an effective way that improves system performance, reduce response time, lessen makespan and utilize resources efficiently. To fulfil these objectives, an effective Tasks Scheduling algorithm is required. The standard Max-Min and Min-Min Task Scheduling algorithms are not able to produce better makespan and effective resource utilization. In this paper, a Resource-Aware Min-Min (RAMM) Algorithm is proposed based on basic Min-Min algorithm. The proposed RAMM Algorithm selects shortest execution time task and assigns it to the resource which takes shortest completion time. If minimum completion time resource is busy, then the RAMM Algorithm selects next minimum completion time resource to reduce waiting time of the task and improve resource utilization. The experiment results show that the proposed RAMM Algorithm produces better makespan and load balance than Max-Min, Min-Min and improved Max-Min Algorithms.