In the paper, we discussed tile evolution of the squeezing, particularly, the effect of damping on higher-order squeezing in the superposition coherent states (Schrodinger cat states), which are generated by superposing a pair of coherent states |α> and |-α) In the initial stage of the field forming, the higher-order squeezing is unstable, the parameters of higher-order squeezing will be oscillatory along with the time elapsing. The states of the field will be Kth-order squeezing or non-squeezing alternatively and tends to stability at last, the absolute value of squeezing parameter reduces and approaches zero. Increasing damping will speed up the evolution process, damping weakens squeezing.