Very large two-photon absorption (TPA) cross sections at the infrared region have been revealed for J-aggregates of asymmetric zinc porphyrin using quantum-chemical calculation. The TPA properties are evaluated for monomer and aggregates of a series of push-pull porphyrins, whose syntheses are known in the literature. The two-photon absorption cross section can be greatly enhanced by increasing the strengths of the electron donor/acceptor. We also present a quantum-chemical analysis on porphyrin aggregates to understand the role of intermolecular interactions and the relationship between structural and collective nonlinear optical properties. It has been observed that the TPA properties change tremendously as monomers undergo J-aggregation and the magnitudes of TPA cross sections are highly dependent on the nature of aggregates. The importance of our results with respect to the design of photonic and photodynamic therapy materials has been discussed.