  Let $[a_1(x),a_2(x),a_3(x),\cdots]$ be the continued fraction expansion of
$x\in (0,1)$. This paper is concerned with certain sets of continued fractions
with non-decreasing partial quotients. As a main result, we obtain the
Hausdorff dimension of the set \[\left\{x\in(0,1): a_1(x)\leq a_2(x)\leq
\cdots,\ \limsup\limits_{n\to\infty}\frac{\log a_n(x)}{\psi(n)}=1\right\}\] for
any $\psi:\mathbb{N}\rightarrow\mathbb{R}^+$ satisfying $\psi(n)\to\infty$ as
$n\to\infty$.
