In this paper, an analytical density of states modeling and simulation study was performed for 3m, 3m+1 and 3m+2 armchair-edge graphene nanoribbon under smaller tensile uniaxial strain. It has been discovered that the irregular variation in DOS as a function of energy when the tensile uniaxial strain is increased from 0% to 3%. In addition, despite to be reduced in terms of energy gap, 3m+1-AGNR is reported to have higher DOS compared to the other families of AGNR while the energy gap opening is confirmed to behave according to its family's behavior.