A new kind of quantum non-Gaussian state with a vortex structure,termed a Bessel-Gaussian vortex state,is constructed,which is an eigenstate of the sum of squared annihilation operators a2 + b2.The Wigner function of the quantum vortex state is derived and exhibits negativity which is an indication of nonclassicality.It is also found that a quantized vortex state is always in entanglement.And a scheme for generating such quantized vortex states is proposed.