  With the twelve-year long observations by {\sl Fermi}-LAT, we discover two
pairs of spin-down state transitions of PSR J1124--5916, making it the second
young pulsar detected to have such behaviors. PSR J1124--5916 shows mainly two
states according to its spin-down rate evolution, the normal spin-down state
and the low spin-down state. In about 80\% of the observation time, the pulsar
is in the normal spin-down state, in which the spin-down rate decreases
linearly and gives a braking index of $1.98\pm0.04$. The two transitions to the
low spin-down state are in MJD 55183--55803 and MJD 56114--56398 respectively,
with fractional amplitudes both $\sim0.4\%$. No significant difference between
the $\gamma$-ray profiles of the two spin-down states is detected, which is
similar to PSR B0540-69, the other young pulsar with state transition detected.
