On the basis of a two-fluid, cold-plasma, linear stability calculation with linear friction between electrons and ions, the growth rate of Alfvén waves is derived from the dispersion relation for a uniformly magnetized plasma, in which the plasma resistivity and a uniform electric current carried by an electron beam are both considered. The growth rate is directly proportional to the plasma resistivity, the electric current density and the value of the parameter ωxpe/Ωe (where ωxpe and Ωe are the electron plasma and cyclotron frequency respectively). Moreover, the growth of Alfvén waves is mainly excited in a direction nearly parallel to the ambient magnetic field. The critical value of the velocity of the electron fluid is just equal to the Alfvén velocity. The results of this paper are compared with those for the linear tearing mode.