Abstarct: Abstract In this research, the mextal-molecule-graphene junctions has been investigated. For the mextal electrode, gold is used, and for the graphene electrode, zigzag graphene and armchair graphene are used. Five molecules of the Alkanedithiol family which are connected to the electrodes by the sulfur atom junction and for each molecule, four junctions are investigated in the form of gold-molecule-gold, gold-molecule-graphene zigzag, gold-molecule-graphene armchair and graphene zigzag-molecule-graphene zigzag has taken. The transmission spectra, current-voltage characteristic, rectification rate and negative differential resistance of the molecular structures are obtained for each structure and the hybrid and non-hybrid junctions as well as the length of the molecule are compared. Electron transfer calculations baxsed on the Density-Functional baxsed Tight-Binding (DFTB) and non-equilibrium Green's function method (NEGF) done. Among the most important results, the following can be mentioned. When a hybrid junction is created, the transmission in negative voltages is different compared to positive voltages, and this difference will cause dissimilar currents, and as a result, rectification occurs. In all junctions, the increase in the length of the molecule caused a decrease in transport and, as a result, a decrease in current. In armchair gold-molecule-graphene hybrid junctions, proper rectification is observed, in addition, the current in almost all structures of this junction is higher than gold-molecule-graphene zigzag hybrid junctions, which makes it a suitable device for making molecular diodes. In zigzag-molecule-graphene-zigzag junctions, at some voltages, the transmission decreases with increasing voltage, which causes the current to decrease while the voltage is increased, and these changes cause negative differential resistance, which can be used in oscillators, active filters, and tunnel diodes. , neon lamps and fluorescent lights should be used.