Theoretical aspects of the electron transport in case of zigzag graphene nanoribbons (ZGNR) have been discussed. We have theoretically formulated the quantum well in the graphene sheet and transport characteristics of ZGNR have been shown. Local density of states (LDOS), charge distribution and transmission behavior have been studied. We have noted in our simulations that edge states depends upon number of atoms(N) along with width in case of finite potential well. Armchair calculation has also been done here.