Remaining Useful Life (RUL) prediction can provide critical information for complex equipment Health States (HS) assessment. Historical long-term HS degradation trends and current short-term HS changes are two key factors affecting RUL prediction. However, most existing deep learning-based RUL prediction methods only consider learning short-term HS change features but ignore learning long-term HS degradation trend features, which limits to improvement of RUL prediction performance. To address this problem, this paper develops a RUL prediction framework based on a combination of Time-Series Auto-Correlation Decomposition (TSACD) and Convolutional Neural Network (CNN), which can learn both long-term and short-term features of mechanical equipment, so that achieves more robust and accurate RUL prediction. First, a novel time-series Auto-Correlation decomposition method is proposed to extract historical long-term features from collected long-term monitoring data. The advantage of TSACD is to highlight the true signal by reinforcing periodic features through Auto-Correlation mechanism and to separate pure trend components using a deep time-series decomposition architecture. Second, the long-term features are mapped to the same space as the short-term HS monitoring data using a group linear layer, which is intended to be aligned and fused with short-term monitoring data. Third, the fused features are fed into a CNN for RUL prediction. Finally, a series of comparison experiments on C-MAPSS dataset validate the outstanding prognostic performance of the proposed method. The experimental results show that the proposed method outperforms the other 16 state-of-the-art RUL prediction methods.