In this study, the multi-quasiparticle triaxial projected shell model (TPSM) is applied to investigate
-vibrational bands in transitional nuclei of
. We report that each triaxial intrinsic state has a
-band built on it. The TPSM approach is evaluated by the comparison of TPSM results with available experimental data, which shows a satisfactory agreement. The energy ratios, B(E2) transition rates, and signature splitting of the
-vibrational band are calculated.