The performance characteristics of aero-engine secondary air system (SAS) critically influence the safe operation and service life of aero-engine. However, they may deviate from the design values due to the uncertainty of geometric parameters and aerodynamic parameters. To quantitatively comprehend and control the influence of random uncertainty, this paper develops a measurement-based Kriging-based uncertainty quantification (UQ) framework of SAS. And the framework is applied to a turbofan’s low-pressure flow path SAS. The measurement data of the labyrinth seals clearance at the beginning and end of a certain turbofan service life cycle is analyzed. It’s found that, as the accumulation of turbofan operating hours, the probability distribution ranges of the labyrinth sealing clearances deviate and expand significantly. Corresponding, the flow rate bled from high-pressure compressor (HPC) and low-pressure rotor axial force also show deviations from the design value on different extent. By repairing the identified key sealing clearances, their probability distributions at the end of the turbofan service life cycle can be restored tending to the initiation. The UQ framework and the case analysis could provide support for the robustness and reliability optimization of aero-engine SAS design.