  We show an inconsistence of the novel 4D Einstein-Gauss-Bonnet gravity by
considering a quantum tunneling process of vacua. Using standard semi-classical
techniques, we analytically study the vacuum decay rate for all allowed cases
in the parameter space. It turns out, without exception, that the theory either
encounters a disastrous divergence of vacuum decay rate, or exhibits a
confusing complex value of vacuum decay rate, or involves an infinitely
instability (a large vacuum mixing). These suggest a strong possibility that
the theory, at least the vacuum of the theory, is either unphysical or
unstable, or has no well-defined limit as $D\rightarrow 4$.
