In this letter we present the extended usage of short-time Chebyshev wave packet method in the laser induced molecular photoionization dynamics. In our extension, the polynomial expansion of the exponential in the time evolution operator, the Hamiltonian operator can act on the wave packet directly which neatly avoids the matrix diagonalization. This propagation scheme is of obvious advantages when the dynamical system has large Hamiltonian matrix. Computational simulations are performed for the calculation of photoelectronic distributions from intense short pulse ionization of K-2 and NaI which represent the Born-Oppenheimer (BO) model and Non-BO one, respectively. (C) 2016 Elsevier B.V. All rights reserved.