An efficient finite-rate chemistry (FRC) model is developed for a preconditioned compressible flow solver. The model uses a point-implicit stiff ODE solver and a correlated dynamic adaptive chemistry algorithm. With respect to the conventional FRC model using the double precision variable coefficient stiff ODE solver, the present work achieves an 8.6 times speed-up for chemistry calculation, and 6.4 times for total computation, when using a 20-species kinetics mechanism for methane/air flames. As an example problem, a piloted partially premixed methane/air jet flame (Sandia Flame D), with a relatively low level of local extinction and re-ignition, is considered, and both the new FRC-large eddy simulation (LES) and flamelet/progress-variable (FPV)-LES are conducted. The FRC-LES approach predicts larger time-averaged flame length, and better agrees with the measured value. This is because the instantaneous high-temperature zone for the FPV-LES case is significantly smaller than it's FRC-LES counterpart, especially in the downstream region. For spatial distribution of time-averaged statistics, the FPV-LES result agrees with the experimental data better. For conditional statistics in the mixture fraction space, the FRC-LES approach provides significantly better predictions. Near the stoichiometric region, in comparison with experimental data and the FRC-LES results, the FPV-LES approach predicts higher radical generation, but lower CO generation and heat release. (C) 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.