The dispersion-free dipole polarizability (α) computations for chlorophyll a (1) and crocin (2) have been achieved by density functional theory (DFT) at B3LYP/ 6-31G(d) level. The measured one-photon absorption (OPA) wavelengths are quite consistence with the theoretically obtained values. Ab-initio quantum chemical calculations (time-dependent Hartree-Fock (TDHF)) have been implemented to reveal the static second hyperpolarizabilities (γ) and dynamic dipole polarizabilities of the title molecules. The examined compounds display γ with non-zero values, introducing their third-order nonlinear optical (NLO) phenomena. The first and second frontier molecular orbitals of the investigated molecules have been also derived from DFT.