Results from three-dimensional (3-D) electromagnetic particle simulations of Alfven waves generated by an electron beam in a nonrelativistic electron-positron plasma are presented. The results show that electrostatic modes are excited due to the beam instability. The bunches of the particles (electrons and positrons) caused by electrostatic waves are directly involved in the generation of Alfven waves. The Alfven waves propagate along the beam as damped solitons accelerating the background particles. The simulation results are in good agreement with theoretical analysis.