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Detecting abnormal crowd motion emerging from complex interactions of individuals is paramount to ensure the safety of crowds. Crowd-level abnormal behaviors (CABs), e.g., counter flow and crowd turbulence, are proven to be the crucial causes of many crowd disasters. In the recent decade, video anomaly detection (VAD) techniques have achieved remarkable success in detecting individual-level abnormal behaviors (e.g., sudden running, fighting and stealing), but research on VAD for CABs is rather limited. Unlike individual-level anomaly, CABs usually do not exhibit salient difference from the normal behaviors when observed locally, and the scale of CABs could vary from one scenario to another. In this paper, we present a systematic study to tackle the important problem of VAD for CABs with a novel crowd motion learning framework, multi-scale motion consistency network (MSMC-Net). MSMC-Net first captures the spatial and temporal crowd motion consistency information in a graph representation. Then, it simultaneously trains multiple feature graphs constructed at different scales to capture rich crowd patterns. An attention network is used to adaptively fuse the multi-scale features for better CAB detection. For the empirical study, we consider three large-scale crowd event datasets, UMN, Hajj and Love Parade. Experimental results show that MSMC-Net could substantially improve the state-of-the-art performance on all the datasets.