Online adaptive radiation therapy (ART) based on real-time magnetic resonance imaging represents a paradigm-changing treatment scheme. However, conventional quality assurance (QA) methods based on phantom measurements are not feasible with the patient on the treatment couch. The purpose of this work is to develop a fast Monte Carlo system for validating online re-optimized tri-60Co IMRT adaptive plans with both high accuracy and speed. The Monte Carlo system is based on dose planning method (DPM) code with further simplification of electron transport and consideration of external magnetic fields. A vendor-provided head model was incorporated into the code. Both GPU acceleration and variance reduction were implemented. Additionally, to facilitate real-time decision support, a C++ GUI was developed for visualizing 3D dose distributions and performing various analyses in an online adaptive setting. A thoroughly validated Monte Carlo code (gPENELOPE) was used to benchmark the new system, named GPU-accelerated DPM with variance reduction (gDPMvr). The comparison using 15 clinical IMRT plans demonstrated that gDPMvr typically runs 43 times faster with only 0.5% loss in accuracy. Moreover, gDPMvr reached 1% local dose uncertainty within 2.3 min on average, and thus is well-suited for ART QA.