We report systematic 31 P-NMR study on iron (Fe)-based superconductors SrFe2(As1−xPx)2 (Sr122AsP), in which a superconducting (SC) transition temperature Tc at x=0.35 increases from Tc=26 K up to 33 K by annealing an as-grown mono-crystalline sample. The present NMR study has unraveled that Tc reaches a highest value of 33 K at x=0.35 around a quantum critical point at which antiferromagnetic (AFM) order disappears. When noting that the SC transition disappears at x=0.6 where the AFM spin fluctuations (SFs) are no longer present, we remark that the onset and increase of Tc are apparently associated with the emergence and enhancement of AFM-SFs, respectively. In the SC state, the residual density of state (RDOS) at the Fermi energy EF in the SC state becomes much smaller for the annealed sample than for the as-grown one, suggesting that some inhomogeneity and/or imperfection for the latter increases RDOS as expected for unconventional SC state with nodal gap. These findings in Sr122AsP are consistent with the unconventional s±-wave Cooper pairing state that is mediated by AFM-SFs. We also discuss other key-ingredients besides the AFM-SFs to increase Tc further.