  In this paper, we prove the $q$-log-convexity of Domb's polynomials, which
was conjectured by Sun in the study of Ramanujan-Sato type series for powers of
$\pi$. As a result, we obtain the log-convexity of Domb's numbers. Our proof is
based on the $q$-log-convexity of Narayana polynomials of type $B$ and a
criterion for determining $q$-log-convexity of self-reciprocal polynomials.
