Prolate-oblate shape phase transition is an interesting topic in nuclear structure, which is useful for understanding the intrinsic interactions between nucleons. Recently, the interacting boson model with SU (3) higher-order interactions was proposed, in which the prolate shape and the oblate shape are not described in a mirror symmetric way. This asymmetric description seems more realistic. The level evolutions, B(E2) values and other important indicators showing the prolate-oblate asymmetric transitions are investigated in detail, and realistic structure evolutions from 180 Hf to 200 Hg are compared. A key finding is that, the average deformation of the prolate shape is nearly twice the one of the oblate shape. These results, together with the successful description of the B(E2) anomaly in 168,170 Os, 172 Pt, the γ-soft properties of 196 Pt, 82 Kr and the normal states of 110 Cd, support the validity of the new model.