  We consider the multicanonical systems $\vert mK_{S}\vert$ of quasi-elliptic
surfaces with Kodaira dimension $1$ in characteristic 2. We show that for any
$m \geq 6$ $\vert mK_{S}\vert$ gives the structure of quasi-elliptic fiber
space, and 6 is the best possible number to give the structure for any such
surfaces.
