Cloud computing represents relatively new paradigm of utilizing remote computing resources and is becoming increasingly important and popular technology, that supports on-demand (as needed) resource provisioning and releasing in almost real-time. Task scheduling has a crucial role in cloud computing and it represents one of the most challenging issues from this domain. Therefore, to establish more efficient resource employment, an effective and robust task allocation (scheduling) method is required. By using an efficient task scheduling algorithm, the overall performance and service quality, as well as end-users experience can be improved. As the number of tasks increases, the problem complexity rises as well, which results in a huge search space. This kind of problem belongs to the class of NP-hard optimization challenges. The objective of this paper is to propose an approach that is able to find approximate (near-optimal) solution for multi-objective task scheduling problem in cloud environment, and at the same time to reduce the search time. In the proposed manuscript, we present a swarm-intelligence based approach, the hybridized bat algorithm, for multi-objective task scheduling. We conducted experiments on the CloudSim toolkit using standard parallel workloads and synthetic workloads. The obtained results are compared to other similar, metaheuristic-based techniques that were evaluated under the same conditions. Simulation results prove great potential of our proposed approach in this domain.