It provides a challenge for remaining useful life prediction due to the complexity of the engine degradation process. Therefore, this paper proposes an improved method for engine remaining useful life prediction with long and short memory neural networks (LSTM) and extraction of health indicators for measured parameters. In order to overcome the limitation of measured parameters, a second-order polynomial approach is implemented to construct novel virtual parameters based on the existing parameters and improve the representativeness of the data to the engine degradation process. Then, random forests are used to score the importance of these parameters on the basis of which the higher rated parameters are filtered to reduce the computational burden. For the hyperparameter optimization problem of LSTM, an improved golden jackal optimization method is proposed in this paper, in which chaotic mapping is used to initialize the population to increase the uniformity of the initial population distribution in space. An adaptive method is introduced to improve the exploration and exploration capabilities of the golden jackal algorithm. Finally, the effectiveness of the proposed method is verified by NASA’s public dataset. The experimental results show that the R2 of the proposed method is greater than 0.99, the error of mean absolute percentage error is within 3%, and the root mean square error is smaller than 4. The proposed method can provide better predicted performance compared with the traditional methods.