Droplet injection methods are widely used in the applications of microelectronic manufacturing, biological engineering, and 3-D printing. This work presents a new jet dispenser driven by a single piezoelectric stack that enables the capability of drop-on-demand patterning under a high working frequency (500 Hz). Due to the special designs of the jet dispenser, a broad range of liquids, whose viscosities span more than four orders of magnitude (21-665 320 cps), can be jetted. Moreover, a coupled Coulomb damping physical model is proposed, which includes an electromechanical and a dynamic model. Both the Coulomb and the fluid-solid damping are considered in the dynamic model. In order to validate the results obtained by using MATLAB/Simulink, the experiments were carried out. The injection performance of this jet dispenser has been tested by employing a self-made jetting platform. The minimum volume of a jetting droplet is about 14.4 nL with liquid wax. The error of volume uniformity among droplets does not exceed 8%, and the error of angle trajectory is about 0.17°. Furthermore, the versatility of the jet dispenser is demonstrated by printing liquid lubricant, food, glue, silver past, and a ceramic slurry in predefined patterns.