A continuous micro-dose administration apparatus includes a needle apparatus, a drug storage apparatus, a piston push rod apparatus, a force accumulating apparatus, an accumulated force release apparatus, and a control apparatus. Under the action of the control apparatus, the accumulated force release apparatus releases a specified piston stroke, the force accumulating apparatus pushes the piston push rod apparatus to move into the drug storage apparatus by the specified piston stroke, and drug liquid in the drug storage apparatus is discharged through the needle apparatus. With the force accumulating apparatus as a power source, the piston body is pushed by means of rotation or direct pushing, a required number of pulses is calculated according to a dose to be infused or a distance moved by the piston, and the control apparatus accurately controls the accumulated force release apparatus to release the specified piston stroke, thereby improving the dose administration accuracy.