Porphyrin is a very important component of natural and artificial catalysis and oxygen delivery in blood. Here, we report that, based on first-principles density-functional calculations, a hydrogen molecule can be adsorbed non-dissociatively onto Ti-, V-, and Fe-porphyrins, similar to oxygen adsorption in heme-containing proteins, with a significant energy gain, greater than 0.3 eV per H(2). The dihydrogen-heme complex will be non-magnetic, as is oxyhemoglobin. In contrast to the backward electron donation of Fe(III)-O(2)(-) in oxyhemoglobin, the dihydrogen binding originates from electron donation from H(2) to the Fe(II). We have identified that the local symmetry of the transition metal center of porphyrins uniquely determines the binding strength, and, thus, one can even manipulate the strength by intentionally and systematically breaking symmetry.