Compared with traditional machining processes, additive manufacturing (AM) has received widespread attention in recent years because of its high degree of modeling freedom. However, due to the multiple manufacturing errors and complex physical state changes involved in the process, the geometric deviation on the AM part surface is a challenge for controlling product geometrical quality. To address this problem, data-driven machine learning (ML) techniques have been widely studied in product quality controlling. However, traditional ML greatly depends on the training sample data, and suffers the risk of violating physical mechanisms due to the lack of domain knowledge. In order to take the best advantage of domain knowledge, prior information and deep learning algorithm, this paper proposes a knowledge-integrated deep learning algorithm and constructs the geometric deviation prediction model of the AM part surface. After that, the method was verified with design of experiments. The results show that compared with the data-driven neural network (DDNN), the knowledge-integrated neural network (KINN) has fewer iterations during the training process, less sample data requirement and more accurate prediction results.