Machining quality prediction is the critical link of quality control in parts machining. With the advent of the Industry 4.0 era, intelligent manufacturing and data-driven technologies bring new ideas for quality control in complex machining processes. Quality control is complicated for multi-process, multi-condition, small-batch, and high-precision parts processing requirements. To solve this problem, this paper proposes a machining quality prediction method based on the machining error transfer network and the grey neural network. Initially, by constructing a processing error transfer network, the error transfer law in part processing is described, and the PageRank algorithm and the influence degree of the nodes are used to determine the critical quality features. Additionally, the problem of low prediction accuracy due to small sample data and multiple coupling relationships is solved using the grey neural network algorithm, and a high accuracy prediction of critical quality features is achieved. Finally, the effectiveness and reliability of the method are verified by the case of medium-speed marine diesel engine fuselage processing. The results indicate that this method not only effectively identifies critical quality features in the machining process of complex parts, but it also maintains a high predictive accuracy for these features, even with small samples and limited data.