The laminar mixed convection flow across the porous square cylinder with the heated cylinder bottom at the axis in the channel has been carried out numerically in this paper using a semi-implicit projection finite element method. The governing equations with the Brinkman–Forcheimer-extended Darcy model for the region of square porous cylinder were solved. The parameter studies including Grashof number, Darcy number, and channel-to-cylinder height ratio on heat transfer performance have been explored in detail. The results indicate that the heat transfer is augmented as the Darcy number and channel-to-cylinder height ratio increase. The buoyancy effect on the local Nusselt number is clearer for $B/H=0.1$ than for $B/H=0.3$ and $B/H=0.5$.