By using a new parametrization way, =(q y-1)/(q-1), the q Boson annihilation operator was defined, and a new q coherent state was constructed. The system Hamiltonian that can produce and maintain the q coherent state was found. We studied the mathematical construction and the quantum fluctuation characteristic of the orthonormalization eigenstates of a q k (k≥1). It is found that the only even q coherent states have usual squeezing effect, and when the parameter q<1, the quantum fluctuation of both quadrature components of the field for each state may be simultaneouly smaller than the minimum uncertainly value (1/4) of the coherent state. These eigenstates have q squeezing.