In this work, a standard solar model is computed with new reaction rates that take into account the exact astrophysical S-factor, S e for the 3He(3He,2p)4He, 3He(α,γ)7Be and 7Be(p,γ)8B reactions. The exact S-factor which is valid for all energies is an improved version of the S-factor in the lower-energy approximation (Yusof and Kassim in Astrophys. Space Sci., 2009b). The effects of these new nuclear reaction rates on the solar neutrino fluxes are then discussed by comparing this model to a solar model computed with the standard NACRE reaction rates (Angulo et al. in Nucl. Phys. A. 656:3, 1999). The new reaction rates are found to decrease the neutrinos flux for 7Be and 8B by about 6% and 16%, respectively. A solar model is also computed with the reaction rates of the LUNA collaboration for 14N(p,γ)15O (Formicola et al. in Phys. Lett. B 591:61, 2004). In this case, a clear decrease of the fluxes for 13N and 15O is observed to be in good agreement with previous results (see e.g. Bahcall et al. in Astrophys. J. 621:L88, 2005).