Remaining useful life (RUL) prediction has been a hotspot topic, which is useful to avoid unexpected breakdowns and improve reliability. Different bearing failure behaviors caused by multiple failure modes may lead to inconsistent feature distribution, which affects the prediction model performance. To accurately predict the RUL of bearing under different failure behaviors, a transferable convolutional neural network (TCNN) is proposed to learn domain invariant features. In the proposed method, a convolutional neural network is employed to extract the degradation features. Then multiple-kernel maximum mean discrepancies are integrated into optimization objective to reduce distribution discrepancy. The trained TCNN can be used to predict RUL by feeding data. Its effectiveness is verified by a run-to-failure bearing dataset. The comparison results reveal that the proposed method avoids the influence of kernel selection, improves the performance of domain adaptation effectively, and achieves a better RUL prediction performance.