In this paper, we consider concerning absolute convergence
of the lacunary Fourier series of several variables
$$
\displaystyle{
f( {\bold x}) \sim \sum_{ {\bold m} \in \Lambda } c_{{\bold m}} 
e^{ i \bold{mx}}
\hspace{1mm},}
$$
where a lattice point set $ \Lambda $ satisfies some gap conditions.
We generalize the result of [2;{\bf Theorem}] in the case of several variables.