Abstract: The iterated fission probability (IFP) method and Contributon-linked eigenvalue sensitivity/uncertainty estimation via track-length importance characterization (CLUTCH) method are commonly used by many Monte Carlo codes for the sensitivity analysis of k-eigenvalue to continuous-energy nuclear data. The memory consumption of the IFP method is huge and the CLUTCH method is proposed to reduce the memory usage of the IFP method. However, it's hard to tally sufficiently-converged importance weighting functions for the mesh-based CLUTCH (CLUTCH-Mesh) method for large-scale problems, such as AP1000 whole core problem, subsequently reducing the accuracy of sensitivity coefficients calculated by the CLUTCH method. Therefore, the function expansion tally (FET) was used to tally importance weighting functions in the CLUTCH (CLUTCH-FET) method in this paper. Legendre polynomial was selected as the basic function of FETs and both segmented FETs with low orders and the global FET with the high order were implemented. During the tally process of FETs, the spatial locations of particles should be projected into domains of definition firstly, and then the tally scores of function expansion coefficients were obtained and accumulated. By averaging function expansion coefficients among inactive cycles, the FET was finished. The FETs were used for both ancestor fission neutrons distribution in original generations and the averaged progenies of the ancestor fission neutron in asymptotic generations. Based on the method mentioned above, the IFP, CLUTCH-Mesh and CLUTCH-FET methods were implemented in Monte Carlo code NECP-MCX. The verifications were conducted among Godiva, Flattop and AP1000 whole core problems by comparing the sensitivity results of CLUTCH-Mesh method, CLUTCH-FET method and the IFP method, whose results were selected as the reference. The numerical results indicate that for small-scale problems, such as Godiva and Flattop problems, the CLUTCH-Mesh and CLUTCH-FET methods are able to calculate the sensitivity results with the same high precision as the IFP method. In addition, the tally efficiency of CLUTCH-Mesh method equals to that of the CLUTCH-FET method and the tally efficiency of these two methods are significantly higher than that of the IFP method. For large-scale problems, such as the AP1000 whole core problem, large bias exists between the sensitivity results of the CLUTCH-Mesh method and those of the IFP method because very large number of particles are needed to obtain sufficiently-converged importance weighting functions. However, the CLUTCH-FET method remains high accuracy and tally efficiency for large-scale problems. The FOM (figure of merit) values of the CLUTCH-FET method can be increased by 5.2 and 6.0 times when compared to those of the IFP method and the CLUTCH-Mesh method, respectively. Therefore, the CLUTCH-FET method is recommended for sensitivity calculation of large-scale problems. Segmented FETs with low orders are more recommended than a global FET with high order to avoid under-fitting or over-fitting problems.