High quality of security is increasingly critical for applications running on heterogeneous distributed systems. However, existing scheduling algorithms for heterogeneous distributed systems disregard security requirements of applications. To address this issue, in this paper, we introduce security heterogeneity concept for our scheduling model in the context of distributed systems. Based on the concept, we propose a novel heuristic scheduling algorithm, or SATS, which strives to maximize the probability that all tasks are executed without any risk of being attacked. Extensive experimental studies using real world traces indicate that the scheduling performance is affected by heterogeneities of security and computational power. Additionally, empirical results demonstrate that with respect to security and performance, the proposed scheduling algorithm outperforms existing approaches under a wide spectrum of workload conditions.