In recent years, deep learning has become prevalent in Remaining Useful-Life (RUL) prediction of bearings. The current deep-learning-based RUL methods tend to extract high dimensional features from the original vibration data to construct the Health Indicators (HIs), and then use the HIs to predict the remaining life of the bearings. These approaches ignore the sequential relationship of the original vibration data and seriously affect the prediction accuracy. In order to tackle this problem, we propose a hard negative sample contrastive learning prediction model (HNCPM) with encoder module, GRU regression module and decoder module, used for feature embedding, regression RUL prediction and vibration data reconstruction, respectively. We introduce self-supervised contrast learning by constructing positive and negative samples of vibration data rather than constructing any health indicators. Furthermore, to avoid the subtle variability of vibration data in the health stage to aggravate the degradation features learning of the model, we propose the hard negative samples by cosine similarity, which are most similar to the positive sample. Meanwhile, a novel infoNCE and MSE-based loss function is derived and applied to the HNCPM to simultaneously optimize a lower bound on mutual information of the positive and negative sample over life cycle, as well as the discrepancy between true and predicted values of the vibration data, such that the model can learn the fine-grained degradation representations by predicting the future without any HIs as labels. The HNCPM is validated on the IEEE PHM Challenge 2012 dataset. The results demonstrate that the prediction performance of our model is superior to the state-of-the-art methods.