A computational study is performed on a chemically reacting laminar boundary layer over a porous horizontal wall with a diffusion flame. The generation of counter-rotating vortices along the flame sheet is observed. Our attention is focused on i)local acceleration, which induces an anomaly in the velocity distributions across the flat plate boundary layer, and ii)the origin of hydrodynamic instability, which may disturb and wrinkle the flame downstream. Results show that when reaction exothermicity is taken into account in the numerical simulation, both the aerodynamic structures and the mass transfer of the chemical species change significantly, especially in the region near the front edge of the burner. Counter-rotating vortices are generated along the flame sheet and are expected to induce hydrodynamic instability. A high pressure zone in front of the leading flame edge and local acceleration are numerically simulated in agreement with experimental observation. Buoyancy plays a negligible role in the behavior of flow and combustion in regions upstream of the burner.