We have theoretically studied the usefulness of ultrashort chirped laser pulses for laser control of photodissociation dynamics with a one-dimensional model system involving a potential well in the excited electronic state. The molecular System we treat in this paper entails three electronic states; a ground electronic state, and two excited electronic states; The ground electronic state is radiatively dipole-coupled with the lower of the-two excited electronic states, while the two excited electronic states are themselves connected by diabatic coupling potential. Previously, ive:found a single linearly chirped ultrashort(in the order of fs) laser pulse can be employed to control photodissociation dynamics according to the sign of the chirp rate: A positively chirped pulse traps the molecule in the excited state potential well, while-a negatively chirped pulse photodissociates the molecule rapidly. In the present paper we take into consideration the influence-of the strength of the diabetic coupling and the reduced mass of the molecular system and show such a-selectivity works best when the diabatic coupling is moderate and the molecular-system is light. We explain these phenomena by a state selective excitation in vibrational states under the condition of adiabatic rapid passage (ARP) population transfer. We solve the integrodifferential equation of the molecular system involving the vibrational states explicitly; which is a quite different approach from that for the atomic case.