Progressive collapse, which is referred to as the collapse of the entire building under local damages, is a common failure mode happened by earthquakes. The collapse process highly depends on the whole structural system. Since, asymmetry of the building plan leads to the local damage concentration; it may intensify the progressive collapse mechanism of asymmetric buildings. In this research the progressive collapse of regular and irregular 6-story RC ordinary moment resisting frame buildings are studied in the presence of the earthquake loads. Collapse process and collapse propagation are investigated using nonlinear time history analyses (NLTHA) in buildings with 5%, 15% and 25% mass asymmetry with respect to the number of collapsed hinges and story drifts criteria. Results show that increasing the value of mass eccentricity makes the asymmetric buildings become unstable earlier and in the early stages with lower number of the collapsed hinges. So, with increasing the mass eccentricity in building, instability and collapse of the entire building occurs earlier, with lower potential of the progressive collapse. It is also demonstrated that with increasing the mass asymmetry the decreasing trend of the number of collapsed beam and column hinges is approximately similar to the decreasing trend in the average story drifts of the mass centers and stiff edges. So, as an alternative to a much difficult-to-calculate local response parameter of the number of collapsed hinges, the story drift, as a global response parameter, measures the potential of progressive collapse more easily.