  We computed the longitudinal proton structure function $F_{L}$, using the
nonlinear Dokshitzer-Gribov-Lipatov-Altarelli-parisi (NLDGLAP) evolution
equation approach at small $x$. For the gluon distribution, the nonlinear
effects are related to the longitudinal structure function. As, the very small
$x$ behavior of the gluon distribution is obtained by solving the Gribov,
Levin, Ryskin, Mueller and Qiu (GLR-MQ) evolution equation with the nonlinear
shadowing term incorporated. We show, the strong rise that is corresponding to
the linear QCD evolution equations, can be tamed by screening effects.
Consequently, the obtained longitudinal structure function shows a tamed growth
at small $x$. We computed the predictions for all detail of the nonlinear
longitudinal structure function in the kinematic range where it has been
measured by $H1$ collaboration and compared with computation Moch, Vermaseren
and Vogt at the second order with input data from MRST QCD fit.
