  In this paper we define direct product of graphs and give a recipe for
obtained probability of observing particle on vertices in the continuous-time
classical and quantum random walk. In the recipe, the probability of observing
particle on direct product of graph obtain by multiplication of probability on
the corresponding to sub-graphs, where this method is useful to determine
probability of walk on complicated graphs. Using this method, we calculate the
probability of continuous-time classical and quantum random walks on many of
finite direct product cayley graphs (complete cycle, complete $K_n$, charter
and $n$-cube). Also, we inquire that the classical state the stationary uniform
distribution is reached as $t\longrightarrow \infty$ but for quantum state is
not always satisfy.
