The problem of steady laminar magnetohydrodynamic (MHD) mixed convection heat transfer about a heated/cooled vertical slender cylinder is studied numerically, taking into account the effects of transverse curvature and viscous dissipation. A uniform magnetic field is applied perpendicular to the cylinder. The resulting governing equations are transformed into the nonsimilar boundary layer equations and solved using the Keller box method. The velocity and temperature profiles as well as the local skin friction and the local heat transfer parameters are determined for different values of the governing parameters, mainly the magnetic parameter, the Richardson number, and the Eckert number. For some specific values of the governing parameters, the results agree very well with those available in the literature. Generally, it is determined that the local skin friction coefficient and the local heat transfer coefficient increase, increasing the Richardson number and the magnetic parameter Mn or decreasing the Eckert number.