Prognostics and health management technology (PHM), a measure to ensure the reliability and safety of the operation of industrial machinery, has attracted attention and application adequately. However, how to use the monitored information to evaluate the degradation of rolling bearings is a significant issue for its predictive maintenance and autonomic logistics. This work presents a reliable health prognosis approach to estimate the health indicator (HI) and remaining useful life (RUL) of rolling bearings. Firstly, to accurately capture the degradation process, a novel health index (HI) is constructed based on correlation kurtosis for different iteration periods and a Gaussian process latency variable model (GPLVM). Then, a multiple convolutional long short-term memory (MCLSTM) network is proposed to predict HI values and RUL values. Finally, we perform experimental datasets of rolling bearings, demonstrating that the presented method surpasses other state-of-the-art prognosis approaches. The results also confirm the feasibility of the presented method in industrial machinery.