  We study viable small-field Coleman-Weinberg (CW) inflation models with the
help of non-minimal coupling to gravity. The simplest small-field CW inflation
model (with a low-scale potential minimum) is incompatible with the
cosmological constraint on the scalar spectral index. However, there are
possibilities to make the model realistic. First, we revisit the CW inflation
model supplemented with a linear potential term. We next consider the CW
inflation model with a logarithmic non-minimal coupling and illustrate that the
model can open a new viable parameter space that includes the model with a
linear potential term. We also show parameter spaces where the Hubble scale
during the inflation can be as small as $10^{-4} $ GeV, $1$ GeV, $10^4 $ GeV,
and $10^8$ GeV for the number of $e$-folds of $40,~45,~50$, and $55$,
respectively, with other cosmological constraints being satisfied.
