  We provide an alternative proof of a sufficient condition for the fundamental
group of the $n^{th}$ cyclic branched cover of $S^3$ along a prime knot $K$ to
be left-orderable, which is originally due to Boyer-Gordon-Watson. As an
application of this sufficient condition, we show that for any $(p,q)$
two-bridge knot, with $p\equiv 3 \text{ mod } 4$, there are only finitely many
cyclic branched covers whose fundamental groups are not left-orderable. This
answers a question posed by D{\c a}bkowski, Przytycki and Togha.
