  We know that the original Schr\"odinger cat states has no amplitude-squared
squeezing. In this paper, we investigate the amplitude-squared squeezing of
Schr\"odinger cat states using postselected von Neumann measurement. The
results show that after postselected von Neumann measurement, the
amplitude-squared squeezing of Schr\"odinger cat states change dramatically and
this can be considered a result of weak value amplification. The squeezing
effect also investigated by studying the Wigner function of Schr\"odinger cat
states after postselected measurement.
