For turbulent flames involving intense turbulence-chemistry interaction, quantifying the uncertainty originating from the parameters of chemical kinetics and physical models leads to a more rigorous assessment of the predictability of simulations. In the present work, a successive dimension reduction framework based on the active subspace (AS) method is formulated to efficiently quantify modeling uncertainties associated with chemical kinetics, and turbulent combustion model parameters in turbulent flame simulations. The approach is demonstrated in simulating a turbulent H-2/O-2 lifted wall-jet flame. The reduction of the high-dimensional kinetic uncertainty space is first achieved through cheap surrogate autoignition tests, and a single active uncertain kinetic variable is identified. Then a one-dimensional active subspace of the uncertainty space consisting of such an active kinetic variable and four turbulent combustion model parameters are further identified using 25 runs of turbulent flame simulations. Finally, the probability distribution function (PDF) of the flame lift-off length is characterized through Monte Carlo simulations within a cheap response surface that is constructed within the active subspace. The components of the active subspace reveal that both chemical kinetics and turbulent mixing are critical for the flame stabilization. Further analysis shows that the uncertainty in the turbulent heat diffusion could change the dominant reactions between R1 (H+O-2 (sic) O+OH) and R9 (H+O-2 (+ M) (sic) HO2 (+ M)) through varying the local temperature in the flame stabilization zone. In addition, comparisons of the PDFs of the flame lift-off length show that the uncertainty induced by chemical kinetics is comparable with that induced by turbulent combustion model parameters. The successive dimension reduction of uncertain physicochemical parameter space via AS enables efficient uncertainty quantification for turbulent flames, meanwhile providing insights into the controlling physiochemical processes. (C) 2020 The Combustion Institute. Published by Elsevier Inc. All rights reserved.