Aiming at the problems of low detection efficiency and accuracy in the health management process of industrial robot axis， a new Health Index （HI） construction method based on action cycle degradation similarity measurement under the background of mechanical axis operation monitoring big data was proposed， and the robot Remaining Useful Life （RUL） prediction was carried out by combining Long Short-Term Memory （LSTM） network. Firstly， MPdist was used to focus on the similarity features of sub-cycle sequences between different action cycles of mechanical axis， and the deviation distance between normal cycle data and degradation cycle data was calculated， so that the HI was constructed. Then， the LSTM network model was trained by HI set， and the mapping relationship between HI and RUL was established. Finally， the MPdist-LSTM hybrid model was used to automatically calculate the RUL and give early warning in time. The six-axis industrial robot of a company was used to carry the experiments， and about 15 million pieces of data were collected. The monotonicity， robustness and trend of HI and Mean Absolute Error （MAE）， Root Mean Square Error （RMSE）， R-Square （ R^{\mathrm{2}} ）， Error Range （ER）， Early Prediction （EP） and Late Prediction （LP） of RUL were tested. The proposed method were compared with the methods such as Dynamic Time Warping （DTW）， Euclidean Distance （ED）， Time Domain Eigenvalue （TDE） combined with LSTM， MPdist combined with RNN and LSTM. The experimental results show that， compared with other comparison methods， the proposed method has the HI monotonicity and trend higher by at least 0.07 and 0.13 respectively， the higher RUL prediction accuracy， and the smaller ER， which verifies the effectiveness of the proposed method.