In this study, a step process of semi-Markovian random walk with delaying barriers at  and levels () and first falling moment of the process into the delaying barrier at -level, , are mathematically constructed, in this case when the random walk happens according to the Laplace’s distribution. It is given a simple form of the Laplace transformation of the distribution of the random variable.  Also the simple formulas for expectation and variance of  are obtained by the means of this Laplace transformation.