Aiming at the requirement of the on-line detailed atomic model in radiation hydrodynamic simulations, we propose a general model, multi-average ion collisional-radiative model (MAICRM), to rapidly simulate the ionization and charge state distribution of hot dense plasma under non-local thermal equilibrium (NLTE) conditions. In this model, an average ion is used to characterize the features of all the atomic states at one single charge state, including the average orbital occupation and the total population of the atomic states. The rate equations for the orbital occupations and the population are derived from the rate equations of the detailed configurations and separated into two sets under the two assumptions: one is the single orbital rate coefficients (including no occupation nor hole number of the relative orbital) that are only dependent on the charge state, and the other is the coupling of the excitation/de-excitation process and ionization/recombination process, which are weak. Namely, the orbital occupation of an average ion is mainly determined by the excitation/de-excitation process under a certain density and temperature; the population of the average ions is determined by the ionization/recombination process with the fixed orbital occupation. The two sets of rate equations are solved sequentially and iteratively until a set of converged orbital occupation and population values is obtained. The interplay between the occupation and the population is implicit in the excitation/de-excitation rate coefficient and ionization/recombination rate coefficient, each of which is a function of electron density and temperature as well as occupation. In this work, using the newly developed method and codes, the mean ionizations and charge state distributions of Fe, Xe and Au plasmas under different plasma conditions are calculated and in good agreement with the experimental results and DCA/SCA calculations. Meanwhile, compared with the DCA/SCA calculations, in which hundreds or thousands of detailed atomic states at each charge state are considered to obtain a converged ionization balance, MAICRM only considers one kind of ion at one single charge state, thus the computational cost of MAICRM is much reduced and lower than that of DCA/SCA. Due to its good degree of accuracy for ionization balance and its low computational cost, MAICRM is expected to be incorporated into the radiation hydrodynamic program to realize the online calculation of detailed nonequilibrium atomic models in the future.