Task execution in cloud computing requires obtaining stored data from remote data centers. Though this storage process reduces the memory constraints of the user’s computer, the time deadline is a serious concern. In this paper, Adaptive Cost-based Task Scheduling (ACTS) is proposed to provide data access to the virtual machines (VMs) within the deadline without increasing the cost. ACTS considers the data access completion time for selecting the cost effective path to access the data. To allocate data access paths, the data access completion time is computed by considering the mean and variance of the network service time and the arrival rate of network input/output requests. Then the task priority is assigned to the removed tasks based data access time. Finally, the cost of data paths are analyzed and allocated based on the task priority. Minimum cost path is allocated to the low priority tasks and fast access path are allocated to high priority tasks as to meet the time deadline. Thus efficient task scheduling can be achieved by using ACTS. The experimental results conducted in terms of execution time, computation cost, communication cost, bandwidth, and CPU utilization prove that the proposed algorithm provides better performance than the state-of-the-art methods.