Lately, deep learning has been extensively investigated for accelerating dynamic magnetic resonance (MR) imaging, with encouraging progresses achieved. However, without fully sampled reference data for training, current approaches may have limited abilities in recovering fine details or structures. To address this challenge, this paper proposes a self-supervised collaborative learning framework (SelfCoLearn) for accurate dynamic MR image reconstruction from undersampled k-space data. The proposed framework is equipped with three important components, namely, dual-network collaborative learning, reunderampling data augmentation and a specially designed co-training loss. The framework is flexible to be integrated with both data-driven networks and model-based iterative un-rolled networks. Our method has been evaluated on in-vivo dataset and compared it to four state-of-the-art methods. Results show that our method possesses strong capabilities in capturing essential and inherent representations for direct reconstructions from the undersampled k-space data and thus enables high-quality and fast dynamic MR imaging.