Abstarct: One of the most important materials for electronic and spintronic devices are graphene nanoribbons that have attracted much attention. Compared to carbon nanotubes, graphene has a simple structure and it is also possible to prepare a lot easier. Graphene is of interest to the semiconductor industry because of the high electron mobility exhibited and it is planar. In this thesis, the electronic, magnetic and transport properties of armchair and zigzag graphene nanoribbons as well as the effects of dopping impurities on the physical properties of nanoribbons will be examined. At first, the electronic and magnetic properties of pure graphene nanoribbons and dopped with transition mextals (Cr, Mn and Fe) , have been investigated by the approach of density functional theory (DFT) and generalized gradient approximation (GGA) with SIESTA computational code. The results show that armchair graphene nanoribbons in its pure form are non-magnetic semiconductor, and zigzag graphene nanoribbons are magnetic mextal in its pure form, dopped with transition mextal atoms with respect to the location of impurity can be converted them to the magnetic or non-magnetic semiconductors or non-magnetic or magnetic mextal. Then, using non-equilibrium Green's function method (NEGF) and generalized gradient approximation (GGA) by computational TRANSIESTA code, transport properties of zigzag and armchair graphene nanoribbons were investigated. The results show that, in armchair graphene nanoribbons by changing the semiconductor electrodes to the mextal electrodes within the micro-ampere current is achieved and in Zigzag graphene nanoribbons current is micro-amp range. The current and simultaneously the best filtering in armchair graphene nanoribbons examined in this study in the five structure and in zigzag graphene nanoribbons in the tirteen structure was observed. Also the NDR phenomenon was observed in some of the examined structures.