A theory of the conformational behavior and analysis of the persistence length of molecular bottle-brushes strongly adsorbed on a flat surface in a good solvent is presented. For long enough side chains we have shown that the adsorption of a small fraction of side chains already leads to significant increase of the stiffness and drastic conformational changes of the brush in comparison with the 3D case. For a symmetrical distribution of the adsorbed side chains with respect to the backbone, the equilibrium conformation of the brush is close to a rod-like one due to the very large stiffness of the molecule. Under certain conditions the excluded-volume interactions of the side chains of an asymmetrical brush can lead to its bending or twisting in spiral. The obtained results are in good agreement with computer simulations.