In the present study the theoretical and numerical results of Rayleigh-Bernard convection in an electrically conducing fluid in the presence of a vertical external magnetic field is reported. The effect of mean flow at the onset of stationary convection and close to the bifurcation is analyzed. The coefficients of the corresponding amplitude equations are analytically calculated and numerical simulations are performed. Finally, the secondary instabilities, such as Eckhaus, zig-zag and skew-varicose at the onset of stationary convection, associated to the roll solution are studied. It is observed that most of the critical modes appear close to the zig-zag instability. (C) 2013 Elsevier Ltd. All rights reserved.