In this study electric current-induced wind forces on a unit lattice of a 10-dimer zigzag graphene nanoribbon (ZGNR) are calculated under different magnitudes of electric field and temperatures. Wind forces are calculated using a semi-classical method where quantum mechanics is integrated into ensemble Monte Carlo simulations by considering energy and momentum conservation in both the transverse and longitudinal directions of graphene nanoribbon (GNR) during the electron-phonon scattering process. First order perturbation theory using the deformation potential approximation was used in the calculation of the scattering rates. The results show that under the same electric field, Joule heating power in a 10-dimer ZGNR is around 3 magnitudes higher than that in metallic single-walled carbon nanotubes and the wind forces are 1 magnitude higher. According to the calculated results, the wind force in the 10-dimer ZNGR is in the order of 0.0073 eV Å-1 under 20 kV at 300 K and it is much lower than the fracture strength of ZGNR based on the results of molecular dynamics simulations. Thus the failure of GNR under an electric current is considered to be mainly due to the Joule heating.