Hybrid cloud is a cost-effective way to address the problem of insufficient resources for satisfying its users’ requirements in a private cloud by elastically scaling up or down its service capability by combining the private cloud and public clouds. However, it is a challenge to schedule tasks on hybrid resources concerning their performance and security requirements. To address the challenge, this paper aims at improving the number of finished tasks with deadline and security requirements and the resource usage cost in heterogeneous hybrid clouds, based on data protection technologies providing various security levels with different overheads for data transfers and task executions in public clouds. We first formulate the problem as a bi-objective binary nonlinear programming (BOBNP) model which is a NP-hard problem. Then, to solve the problem in polynomial time, we propose a Task Scheduling method concerning Security (TSS). To improve the cost, TSS iteratively assigns the task requiring maximum cost of public resources to the local cluster, and rents the public resource with the best cost-performance ratio first for outsourced tasks. To complete as many tasks as possible, TSS assigns tasks cannot be finished by public clouds to the local cloud at first, and employs the idea of Least Slack Time First (LSTF) with Earliest Deadline First (EDF) in each computing node. Extensive experimental results show the superior performance of TSS in satisfying task requirements, and in resource efficiency when task deadlines are not too tight, compared with four hybrid cloud scheduling methods proposed recently.