Thickness pure-shear mode film bulk acoustic wave resonators (FBARs) made of (1120) textured ZnO films have been fabricated. We also have fabricated FBAR structure consisting of two layers of the (1120) textured ZnO film with opposite polarization directions. This FBAR structure operated in second overtone pure-shear mode and allowed shear-mode FBARs at higher frequency. The effective electromechanical coupling coefficients k2 of pure-shear mode FBAR and second overtone pure-shear mode FBAR in this study were found to be 3.3% and 0.8%, respectively. The temperature coefficient of frequency (TCF) of thickness extensional mode FBAR, pure-shear mode FBAR, and second overtone pure-shear mode FBAR were measured in the temperature range of 10-60 degrees C. TCF values of -63.1 ppm/degrees C, -34.7 ppm/degrees C, and -35.6 ppm/degrees C were found for the thickness extensional mode FBAR, the pure-shear mode FBAR, and the second overtone pure-shear mode FBAR, respectively. These results demonstrated that pure-shear mode ZnO FBARs have more stable temperature characteristics than the conventional thickness extensional mode ZnO FBARs.