A sub-nanometric closed-loop displacement control system for piezoelectric transducers has been set up based on an optical frequency comb, an external cavity diode laser and a Fabry-Perot interferometer. The external cavity diode laser is locked to the optical frequency comb, so that the optical frequency can be set precisely in the working range by tuning the repetition frequency of the optical frequency comb. As a sensor of the piezoelectric transducer, the Fabry-Perot cavity is locked to the external cavity diode laser by means of the Pound-Drever-Hall locking technique. With the aid of precisely controlling the diode laser frequency, displacements of the piezoelectric transducer can be obtained with a sub-nanometric resolution. Experimental results show that the Allan deviation of the diode laser frequency is 1.68×10-12 after locked to the optical frequency comb. The displacement range of 4.8 μm can be generated by the piezoelectric transducer through continuously and precisely tuning the diode laser frequency in the range of 30.9496 GHz. Meantime, the displacement resolution of 450 pm is achieved by scanning the repetition frequency of the optical frequency comb at a step of 3.75 Hz. Besides, the hysteresis characteristic of the piezoelectric transducer is measured using this system. Compared to those methods based on heterodyne interferometers to calibrate the displacement of piezoelectric transducers, the nonlinear errors are eliminated and the measurement results are traceable to an Rb clock.