  We establish a $q$-analogue of Sun--Zhao's congruence on harmonic sums. Based
on this $q$-congruence and a $q$-series identity, we prove a congruence
conjecture on sums of central $q$-binomial coefficients, which was recently
proposed by Guo. We also deduce a $q$-analogue of a congruence due to Apagodu
and Zeilberger from Guo's $q$-congruence.
