This study presents a novel method for separating images into piecewise smooth (cartoon) and texture parts, exploiting both the variational mechanism and Yves Meyer's modelling principle for oscillating patterns. The basic idea presented in this study is the use of total generalised variation (TGV) to model the cartoon components, and its dual TGV* for the oscillation components. Moreover then, the proposed model is numerically implemented by using alternating direction method. Comparative experiments show that the proposed model can better separate cartoon from texture and well preserve small-scale texture information, at the same time reduce efficiently the staircase effects caused by the classical total variation regularisation in the cartoon components.