Rolling bearings are indispensable parts in mechanical equipment, and predicting their remaining useful life is critical to normal operation and keep equipment in good repair. However, the complex characteristics of bearings make it difficult to describe their degradation characteristics. To address this issue, a novel method that combines an automatic feature combination extraction mechanism with a gated recurrent unit (GRU) network that has a residual multi-head attention mechanism for rolling bearing life prediction is proposed. Firstly, the automatic feature combination extraction mechanism is used to learn the degradation representation of the bearing vibration signal in the time domain, frequency domain, and time–frequency joint domain, and automatically extract the optimal bearing degradation feature combination. Then, the GRU network with residual multi-head attention mechanism is developed to weight and distinguish the learned degradation features, thereby improving the network’s attention to important bearing degradation features. In the end, the proposed method is validated on the prediction and the health management of systems dataset and compared to other advanced approaches. The experimental results show that the proposed method can effectively capture the complex and dynamic features of rolling bearings and has high accuracy and generalization ability in rolling bearing life prediction.