A flamelet tabulation method for partially premixed flames is proposed, in which partially premixed flamelets are incorporated as the archetypal flamelet elements. This method considers triple flame structures with both the partial premixing of fuel in the oxidizer side and the partial premixing of oxidizer in the fuel side, by replacing the pure-air and pure-fuel in the counterflow diffusion flame with a range of fuel-lean and -rich mixtures, respectively. The thermo-chemical quantities in the partially premixed flamelet are stored in a four-dimensional flamelet library as a function of the mixture fraction Z, describing the mixing process, the reaction progress variable Y-PV, describing the progress of reactions, and the trajectory variables Y-F and Y-O. characterizing the partial premixings of fuel and oxidizer, respectively. The performance of the proposed partially premixed flamelet tabulation (PPFT) method is evaluated through both a priori and a posteriori tests on laminar tribrachial flames with different mixture fraction gradients. The PPFT results are compared with those from a premixed flamelet tabulation (PFT) method and a diffusion flamelet tabulation (DFT) method. It is found that the combustion-mode-sensitive species such as CO and H-2 can be accurately predicted by the PPFT method for both the low and high mixture fraction gradient flame cases, which cannot be well predicted by the PFT and DFT methods. (C) 2018 The Combustion Institute. Published by Elsevier Inc. All rights reserved.