The reliability of a Grid resource site will affect the execution performance of tasks on the site, which will bring effect on the queuing time of other tasks on this site. Repairable queuing system was used to describe the reliability of Grid resource sites, and the queuing time of each site in steady-state could be obtained by solving this model. A queuing time aware dynamic Grid workflow scheduling (QTADGWS) algorithm was proposed,and the corresponding dynamic Grid workflow scheduling system was designed. A lot of simulation experiments in different scenarios with different parameter setups have been done based on GridSim. The experimental results indicated that QTADGWS could achieve better performance on makespan and average waiting time than HEFT and CPOP algorithms.