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In a grid workflows, fixed-time constraints are often set at some activities to guarantee that the corresponding activities and finally the overall workflow can be timely completed. At the run-time stage, activity completion durations can vary which may lead to the violations of some fixed-time constraints. Therefore, the workflow needs to be monitored at the run-time so that some temporal violations can be identified timely and consequently some exception handling actions can be taken in time. However, existing temporal verification strategies conduct some unnecessary computations and comparisons which impact the efficiency of overall temporal verification. To address this problem, we present a global-time-offsets based temporal verification approach. With our approach, the time cost for dynamic verification of the fixed-time constraints will be reduced. The experimental result further demonstrates that our approach is more efficient than others.