The largest C-eigenvalue of a piezoelectric tensor determines the highest piezoelectric coupling constant. In this paper, we first provide a new C-eigenvalue localization set for a piezoelectric-type tensor and prove that it is tighter than some existing sets. And then, we present a direct method to find all C-eigentriples of a piezoelectric-type tensor of dimension 3. Finally, we show the effectiveness of the direct method by numerical examples.