This paper presents an investigation for magnetohydrodynamics (MHD) thermocapillary Marangoni convection heat transfer of an electrically conducting power-law fluid driven by temperature gradient. The surface tension is assumed to vary linearly with temperature and the effects of power-law viscosity on temperature fields are taken into account by modified Fourier law for power-law fluids (proposed by Pop). The governing partial differential equations are converted into ordinary differential equations and numerical solutions are presented. The effects of the Hartmann number, the power-law index and the Marangoni number on the velocity and temperature fields are discussed and analyzed in detail.