  The main purpose of this paper is to introduce lacunary strong geometric
zweier convergent sequence spaces $N_{\theta }^{0}
\left[Z\left(G\right)\right]$, $N_{\theta } \left[Z\left(G\right)\right]$,
$N_{\theta }^{\infty } \left[Z\left(G\right)\right]$consisting of all sequences
$x=\left(x_{k} \right)$such that $\left[Z\left(G\right)\right]x$ are in the
spaces $N_{\theta }^{0} ,N_{\theta } {\rm and\; }N_{\theta }^{\infty } $
respectively, which are normed. We prove certain topological properties of
these spaces and compute their lacunary stastical zweier convergence.
