To address the insufficient consideration of safety, the lack of temporal feature extraction, and the limited generalization ability in aircraft fuel-flow prediction, a safety-constrained LSR-TSO-SVR method for fuel flow prediction is proposed on the basis of A320 quick access recorder (QAR) data. The hyperparameters of support vector regression (SVR) were optimized by an improved tuna swarm optimization (TSO) algorithm. Lagged and sliding-window enhanced regression (LSR) and safety hard constraints were incorporated. An aircraft fuel-flow prediction model was then constructed. The results show that, in terms of accuracy, the LSR-TSO-SVR model achieves an average prediction error rate of only 0.94% for the A320, and the prediction accuracy of total fuel consumption reaches 99.97%, which is significantly better than those of the conventional SVR and extreme learning machine (ELM) models. In terms of generalization ability, the prediction error rates for the B737-900ER and C919 are 1.62 %and 1.19%, respectively, which indicates that cross-aircraft-type fuel flow prediction can be achieved by this method. In terms of safety, the predefined safety constraints are satisfied by the A320, B737-900ER, and C919.