This work focuses on the task of privacy-preserving action recognition, which aims to protect individual privacy in action videos without compromising recognition performance. Despite recent advancements, existing privacy-preserving action recognition models still struggle with video domain shifts. To address this challenge, this work aims to develop transferable privacy-preserving action recognition models, by leveraging labeled videos from the source domain and unlabeled videos from the target domain. This work contributes a novel method named GenPriv, which improves the transferability of privacy-preserving models by generative decoupled learning. Inspired by the fact that privacy-sensitive information in action videos primarily comes from the static human appearances, our GenPriv decouples video features into static and dynamic aspects and then removes privacy-sensitive content from static action features.We propose a generative architecture named ST-VAE, complemented by Spatial Consistency and Temporal Alignment losses, to enhance decoupled learning. Experimental results on three benchmarks with diverse domain shifts demonstrate the effectiveness of our proposed GenPriv.