This paper is devoted to investigating the description of the q-deformed multiple-trapping equation for charge carrier transport in amorphous semiconductors. For this, we at first modified the multi–trapping model (MTM) of charge carriers in amorphous semiconductors from time-of-flight (TOF) transient photo-current in the framework of the q-derivative formalism, and then, we have constructed, our simulated current by using a method based on the Laplace method. This method is implemented in a program proposed recently by [14] which allows us to construct a current using the Padé approximation expansion.