The pair coherent state evolution during a parametric frequency conversion is analyzed.And the wavefunction of the evolving pair coherent state in configuration space is obtained.It is found that the state may become a modified Bessel-Gaussian vortex state with topological charge index q which is a new non-Gaussian state.In coherent state representation such a modified Bessel-Gaussian vortex state is an eigenstate of sum of squared two-mode annihilation operators a~2 +b~2.The result obtained in this paper p...