Micro characteristics is essential for radar target recognition. Micro-motion is defined as some dynamics of a target except its main bulk translation. In general, micro-motions are modelled as the sinusoidal forms. However, micro-motions in reality should include more types of movement forms besides the sinusoidal one. This paper establishes the simplest coordinate system according to direction of movement of the target to represent complex micro-motion, so as to achieve approximately simplified model analysis of micro-motion. The mathematical formulas of micro-Doppler induced by targets with arbitrary micro-motion are derived, and examples of several basic and typical micro-motion types are given. Experimental results based on both simulated and measured data validate the effectiveness of the proposed theoretical model.