Summary: This paper is concerned with the following third-order boundary value problem with integral boundary conditions \[ \begin{gathered} u'''(t)+ f(t,u(t), u'(t))= 0,\quad t\in [0,1],\\ u(0)= 0,\quad u'(0)= \int^1_0 g_1(t) u'(t)\,dt,\quad u'(1)= \int^1_0 g_2(t) u'(t)\,dt,\end{gathered} \] where \(f\in C([0,1]\times [0,+\infty)\times [0,+\infty), [0,+\infty))\) and \(g_i\in C([0,1], [0,+\infty))\), \(i= 1,2\). The existence of monotone positive solution to the above problem is obtained when \(f\) is superlinear or sublinear. The main tool used is the Guo-Krasnoselskii fixed point theorem.