ABSTRACT:In this work, we first aim to realize the complete laser-induced photodissociation of the OH molecule, and then intend to control the wavepacket generated on the continuum state, i.e., to achieve the laser control of the abovethreshold dissociation (ATD) spectrum. To numerically solve the Schrö dinger equation, we adopt the split operator method (SOM), which conserves the norm of the state vector, and can treat both discrete and continuum states simultaneously and correctly. This photodissociation process induced by the multiphoton absorption involves the ATD spectrum due to the continuum-continuum transition by the intense electric field. First, we investigate the detailed mechanism of the complete photodissociation with the one-color laser pulse by changing the laser parameters. Then, we investigate the control of the ATD spectrum by using the two-color laser field, where we focus on the role of the relative phase and position of two laser pulses. To analyze the population of both discrete and continuum states involved in the resultant wavepacket, we show the effective method by means of the quasicontinuum state on the Morse potential obtained by numerically diagonalizing the Fourier grid Hamiltonian (FGH).