  In this article we present a refinement of the base point free theorem for
threefolds in positive characteristic. If $L$ is a nef Cartier divisor of
numerical dimension at least one on a projective Kawamata log terminal
threefold $(X,\Delta)$ over a perfect field $k$ of characteristic $p \gg 0$
such that $L-(K_X+\Delta)$ is big and nef, then we show that the linear system
$|mL|$ is base point free for all sufficiently large integer $m>0$.
