Studies on self-supervised visual representation learning (SSL) improve encoder backbones to discriminate training samples without labels. While CNN encoders via SSL achieve comparable recognition performance to those via supervised learning, their network attention is under-explored for further improvement. Motivated by the transformers that explore visual attention effectively in recognition scenarios, we propose a CNN Attention REvitalization (CARE) framework to train attentive CNN encoders guided by transformers in SSL. The proposed CARE framework consists of a CNN stream (C-stream) and a transformer stream (T-stream), where each stream contains two branches. C-stream follows an existing SSL framework with two CNN encoders, two projectors, and a predictor. T-stream contains two transformers, two projectors, and a predictor. T-stream connects to CNN encoders and is in parallel to the remaining C-Stream. During training, we perform SSL in both streams simultaneously and use the T-stream output to supervise C-stream. The features from CNN encoders are modulated in T-stream for visual attention enhancement and become suitable for the SSL scenario. We use these modulated features to supervise C-stream for learning attentive CNN encoders. To this end, we revitalize CNN attention by using transformers as guidance. Experiments on several standard visual recognition benchmarks, including image classification, object detection, and semantic segmentation, show that the proposed CARE framework improves CNN encoder backbones to the state-of-the-art performance.