Abstract: Grid scheduling and resource management potentially involve the interaction of many human players such as end users and resource administrators. Such players result in different, often contradictory, criteria and make the process of mapping jobs to resources difficult or even impossible. Focusing on the independent jobs, the multiobjective job scheduling problem of multi-QoS constraints is proposed and transformed to the general multiobjective combinatorial problem. An advanced evolutionary algorithm is put forward to solve multiobjective grid job scheduling. The evolutionary technique is used to find the non-dominated set of solutions and distribute them uniformly in the Pareto front so that the best compromise scheduling solution can be found. It is shown via simulation that the algorithm performs better than the QoS-Min-min and QoS-Sufferage in the user-QoS performances such as time-dimension, reliability-dimension, security-dimension QoS utilization and the system-QoS performance such as dropped job numbers.