Summary: A two-dimensional MHD stagnation-point flow with variable viscosity is studied. The plate is placed a relatively static magnetic field of \(H_0\), the Navier-Stokes equations are calculated, where viscosity is considered as a function of temperature. The governing Navier-Stokes equations for the MHD stagnation-point flow with variable viscosity were obtained through physical analysis. By using similarity transformation, the governing equations are firstly transformed into the ordinary differential equations (ODEs). Numerically the effects of magnetic strength and temperature changes to the skin friction coefficient, heat transfer near the wall and flow field characteristics are analyzed, and the trend of velocity, magnetic field and temperature field with different parameters are also obtained.