The monitoring of surface quality in machining is of great practical significance for the reliability and life of high-value products such as rocket, spacecraft and aircraft, particularly for their assembly interfaces of these products. Surface roughness is an important metric to evaluate the surface quality. The current research of online surface roughness prediction has the following limitations. The effect of the varying tool wear on the surface roughness is rarely considered in machining. In addition, the deteriorating trend of surface roughness and tool wear is different under variable cutting parameters. Prediction models trained under one set of cutting parameters fail when cutting parameters change. This paper proposes a surface roughness prediction method considering the varying tool wear under variable cutting parameters. A stacked autoencoder and long short-term memory network (SAE-LSTM) is designed as the basic surface roughness prediction model that uses tool wear conditions and sensor signals as the input. The transfer learning strategy is applied on SAE-LSTM such that the surface roughness online prediction under variable cutting parameters can be realized. Machining experiments for the assembly interface (Ti6Al4V material) of the aircraft’s vertical tail are conducted and the monitoring data are used to validate the proposed method. Ablations studies are carried out to evaluate the key modules of the proposed model. The experimental results show that the proposed method outperforms other models and well track the true surface roughness over time.