Most of the existing job scheduling algorithms for grids have ignored the security problem with a handful of exceptions. Moreover, existing algorithms using fixed-number job replications will consume excessive resources when grid security level changes dynamically. In this paper, a Security Aware and Fault Tolerant Scheduling (SAFTS) algorithm based on adaptive replication is proposed which schedules the jobs by matching the user security demand and resource trust level and the number of the job replications changes adaptively with the dynamic of grid security. In experiments on RSBSME (Remote Sensing Based Soil Moisture Extraction) workload in a real grid environment, the average job scheduling success rate is 97%, and average grid utilization is 74%. Experiment results show that performance of SAFTS is better than non-security-aware and fixed-number job replication scheduling algorithms and SAFTS is fault-tolerant and scalable.