In this paper, the quantum statistical properties of the superposition state,a｜ β〉+beiφ｜mβeiδ〉,which involves two arbitrary coh erent states, are investigated. The results show that this kind of super-positio n states generally exhibits squeezing effect or anti-bunching effect. The quantu m effects of the superposed state depend on β2 and the amplitude coe fficient m, as well as the changes of the phase difference between two coherent states δ, and the phase difference between two superposition coefficients φ al so plays an important role in squeezing or anti-bunching effects.