We present a novel electro-optically tuned external-cavity diode laser (ECDL) that utilizes a volume Bragg grating (VBG) as the frequency selective feedback element and a piece of high electro-optic coefficient Lead Lanthanum Zirconate Titanate (PLZT) transparent ceramic as the frequency tuning element. By adjusting the voltage applied onto the PLZT, a single-mode frequency tuning range of 2.5GHz without mode hoping is achieved. The laser wavelength is around 810.0nm with the line-width of 19MHz and the side mode suppression ratio (SMSR) of 37dB. The advantages of combining a VBG and PLZT transparent electro-optic ceramic is that the laser frequency can be tuned finely and rapidly in a range of longitudinal mode spacing without mode hoping. Moreover, the wide-range coarse frequency tuning of 32.7 GHz can also be realized by changing the angle of incident light beam.