In the paper the approximate solution of a partial differential-difference equation is constructed using the two dimensional operational calculus introduced by T. Ogata ([4]) and the results of J. Wloka [8] for ordinary differential-difference equations. In Section 4, an estimate is given for the error of approximation in the space $\mathcal F_0$ of the Mikusiński operator field $\mathcal F$ and also obtained is that the sequence of approximate solutions $\{x_n\}$ converges to the exact solution in the convergence type $\mathrm I'$ (observed by T. Boehme [1] and J.Burzyk [2]). If the exact and the approximate solutions belong to the space $\mathcal L$ of locally integrable functions, then it is obtained that the sequence of the approximate solutions converges to the exact solution in $\mathcal L$.