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$H$.