  In this paper, we study the singularities of a general hyperplane section $H$
of a three-dimensional quasi-projective variety $X$ over an algebraically
closed field of characteristic $p>0$. We prove that if $X$ has only canonical
singularities, then $H$ has only rational double points. We also prove, under
the assumption that $p>5$, that if $X$ has only klt singularities, then so does
$H$.
