  This paper is concerned with the Vlasov-Poisson-Boltzmann system for plasma
particles of two species in three space dimensions. The Boltzmann collision
kernel is assumed to be angular non-cutoff with $-3<\gamma<-2s$ and $1/2\leq
s<1$, where $\gamma$, $s$ are two parameters describing the kinetic and angular
singularities, respectively. We establish the global existence and convergence
rates of classical solutions to the Cauchy problem when initial data is near
Maxwellians. This extends the results in \cite{DYZ-h, DYZ-s} for the cutoff
kernel with $-2\leq \gamma\leq 1$ to the case $-3<\gamma<-2$ as long as the
angular singularity exists instead and is strong enough, i.e., $s$ is close to
1. The proof is based on the time-weighted energy method building also upon the
recent studies of the non cutoff Boltzmann equation in \cite{GR} and the
Vlasov-Poisson-Landau system in \cite{Guo5}.
