Aircraft engine failures or damages not only incur substantial financial losses but also present risks of injuries or even fatalities. Hence, it is of utmost importance to devise an effective method to predict potential failures in advance, thereby mitigating accidents and minimizing losses. This paper proposes a novel approach that combines a principal component analysis (PCA) with similarity methods to establish a degradation trajectory database and predict the remaining useful life (RUL) of new engines by identifying similar trajectories. Firstly, the data dimensionality is reduced using a PCA to create a health indicator. The validity of the reduced data is confirmed by calculating the Spearman correlation coefficient between the health indicator and the system RUL. During the similarity comparison process, the Manhattan distance is employed for the similarity calculation, and parameter optimization is performed on the length of selected time segments and the number of chosen similar trajectories to optimize the similarity of RUL prediction model, resulting in the optimal prediction results among all engine test sets. Notably, this paper introduces the feasibility of employing the Manhattan distance in similarity method-based prediction, which is superior to the commonly used Euclidean distance calculation method found in most literature. This finding offers innovative ideas and perspectives for advancing RUL prediction methodologies. By adopting the proposed approach, the occurrence of accidents and losses associated with aircraft engine failures can be substantially reduced, leading to enhanced safety and economic benefits.