Cloud computing is an advanced internet resources network that is used by many users remotely. The resources include software, hardware, and various applications. The main challenge in cloud computing is task scheduling due to numerous requests are generated simultaneously from remote locations. To overcome this challenge, task scheduling algorithms are designed that appropriately arrange the tasks. In the literature, metaheuristic algorithms have been deployed for optimal task scheduling. The most popular algorithms are genetic algorithm, particle swarm, and cuckoo search algorithm. However, if the initial population of these algorithms is properly not defined then it is easily trapped into the local optimal solution and causes low precision. In this paper, we have overcome this issue and designed an improved cuckoo search algorithm. In the proposed method, the initial population is defined using the chaotic map algorithm and after cuckoo search algorithm is applied to determine optimal task scheduling. The experimental results show that the proposed method is superior in terms of convergence rate, makespan, average waiting time, and average turnaround time as compared to the existing algorithm.