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In the framework of the FP7 Euratom project FREYA, the Serpent Monte Code was used to characterize a number of critical VENUS-F core configurations. Several neutronic parameters calculated by Serpent were compared to the available experimental data and reported in a previous study. Although a generally reasonable agreement between the calculated and experimental values was obtained, the study also revealed some important issues related to the modeling results such as a systematic overestimation of reactivity and a systematic underestimation of U238 to U235 fission rate ratio (designated as F28/F25 spectral index). The objective of the current follow-up study is to assess the impact of nuclear data uncertainties on the Monte Carlo estimates of reactivity and spectral indices. The analysis is carried out for two critical VENUS-F cores using a recently upgraded version of Serpent which is capable to perform sensitivity analysis, based on the collision history method and to propagate and quantify nuclear data uncertainties using multi-group covariance libraries in an automated way. The criticality calculations were performed using the ENDV/B-VII.1 based cross sections while the uncertainties due to nuclear data were obtained using 56-group neutron cross section covariance library from the SCALE-6.2 package. The estimated uncertainties due to nuclear data are of the order of 2200 pcm and 8% on k-eff and F28/F25 spectral index, respectively. It was found that the major contributor to the k-eff uncertainty is the capture cross section of U235. In the F28/F25 case, the total uncertainty is dominated by inelastic scattering cross section of U238, fission spectrum of U235, and capture cross section of U235.