This article presents hydrodynamics simulation of multi-steady states and mode transition by DC-beam-injected gas discharge, and provides a model approach to hysteresis and distinct forms of multi-steady states. The critical transition conditions of the three discharge modes (temperature limited mode, Langmuir mode, and space charge limited mode) are estimated to be dependent on the gas pressure and the filament temperature. Various forms of the multi-steady states in gas discharge can be uniformly explained by the displacement of the mutant positions. The simulation results are in a good agreement with those of the experiments.