Task scheduling is one of the key techniques for effective and reliable resource usage in cloud computing. In this paper, we designed a hybrid heuristic scheduling that employed particle swarm optimisation (PSO) and least accumulated slack time to respectively address the problem of assigning tasks to servers and the problem of the task scheduling for multi-core servers, to maximise the service level agreement (SLA) satisfaction for resource efficiency improvement and task execution in heterogeneous clouds with deadline constraints. Experimental results show that our method can complete up to 112.5% more tasks, compared with several classical and state-of-art task scheduling methods.