  Non-fermi liquid and unconventional quantum critical points (QCP) with strong
fractionalization are two exceptional phenomena beyond the classic condensed
matter doctrines, both of which could occur in strongly interacting quantum
many-body systems. This work demonstrates that using a controlled method one
can construct a non-Fermi liquid within a considerable energy window based on
the unique physics of unconventional QCPs. We will focus on the
"nearly-marginal non-Fermi liquid", defined as a state whose fermion
self-energy scales as $\Sigma_f(i \omega) \sim i
\mathrm{sgn}(\omega)|\omega|^{\alpha}$ with $\alpha$ close to $1$ in a
considerable energy window. The nearly-marginal non-fermi liquid is obtained by
coupling an electron fermi surface to unconventional QCPs that are beyond the
Landau's paradigm. This mechanism relies on the observation that the anomalous
dimension $\eta$ of the order parameter of these unconventional QCPs can be
close to $1$, which is significantly larger than conventional Landau phase
transitions, for example the Wilson-Fisher fixed points. The fact that $\eta
\sim 1$ justifies a perturbative renormalization group calculation proposed
earlier. Various candidate QCPs that meet this desired condition are proposed.
