In this paper, we present Dynamic Normalization and Relay (DNR), a meta learning normalization method, to augment the spatial-temporal representation learning of Convolutional Neural Networks (CNNs) for video action recognition. To explore the potentials of cross-temporal and cross-layer feature distribution dependencies for estimating accurate layer-wise normalization parameters of a certain layer, DNR introduces two normalization relay modules. Specifically, they are encapsulated into a shared and efficient Long Short Term Memory (LSTM) structure conditioned on the current input features as well as the normalization parameters estimated from the neighboring frames at the same layer and from the whole sequence at the preceding layers respectively. We first plug DNR into prevailing 2D CNN backbones and test its performance on public action recognition datasets including Kinetics and Something-Something. Experimental results show that DNR brings large improvements to the baselines, achieving over 4.4