Steady laminar mixed convection boundary layer flow past a horizontal circular cylinder with constant wall heat flux, immersed in a viscous and incompressible fluid of temperature-dependent viscosity is considered in this study. The governing partial differential equations were transformed using non-similar transformation and then solved numerically by an implicit finite-difference scheme known as the Keller-box method. The effects of temperature-dependent viscosity parameter θr on the flow and heat transfer characteristics were examined for various values of Prandtl number, Pr and the mixed convection parameter, λ. It was found that for both assisting and opposing flows, as θr increases, the local skin friction coefficient increases while the wall temperature decreases for air but for water, the local skin friction coefficient decreases then slightly increases while temperature decreases.