The scaling behavior of band gaps and fundamental quantities of exciton, i.e., reduced mass, size, and binding strength, in three families of quasi one-dimensional graphene nanoribbons with hydrogen passivated armchair shaped edge (AGNRs) are comprehensively investigated by density functional theory with quasi-particle corrections and many body, i.e., electron-hole, interactions. Compared with single-walled carbon nanotubes (SWCNTs) where the scaling character features a single exponent, each family of AGNRs has its own single exponent, due to its intrinsic zero curvature, which also accounts for the absent "family spreading" of optical transition energies in the smaller width region in the Kataura plots of AGNRs as compared to those of SWCNTs. Moreover, the scaling relation between exciton binding strength and the geometric parameter is established.