  A path integral with BRST symmetry can be formulated by summing the
Gribov-type copies in a very specific way if the functional correspondence
between $\tau$ and the gauge parameter $\omega$ defined by $\tau (x) = f(
A_{\mu}^{\omega})$ is ``globally single valued'', where $f( A_{\mu}^{\omega}) =
0 $ specifies the gauge condition. A soluble gauge model with Gribov-type
copies recently analyzed by Friedberg, Lee, Pang and Ren satisfies this
criterion. A detailed BRST analysis of the soluble model proposed by the above
authors is presented. The BRST symmetry, if it is consistently implemented,
ensures the gauge independence of physical quantities. In particular, the
vacuum (ground) state and the perturbative corrections to the ground state
energy in the above model are analysed from a view point of BRST symmetry and
$R_{\xi}$-gauge. Implications of the present analysis on some aspects of the
Gribov problem in non-Abelian gauge theory, such as the $1/N$ expansion in QCD
and also the dynamical instability of BRST symmetry, are briefly discussed.
