This paper presents a new micro assembly system, which is composed of a micro gripper, a micro remote center compliance (RCC) unit, a voice coil motor-driving mechanism and precision motion stages. The micro gripper is actuated by two shape memory alloy (SMA) wires, and its grip is 1 mm. The micro RCC unit has low translational and rotational stiffness sufficient for micro parts assembly. The voice coil motor-driving mechanism can generate linear motion with an adjustable stiffness, and it can also measure external force in the moving direction. An algorithm for the automatic assembly of micro parts is also proposed, and assembly experiments are performed.