We have investigated analytically and numerically on both the generalized dimension D sub(n) and the fractal dimensionality f sub($alpha$) in the dissipative Willbrink map. and discussed both the mode-locking phenomenon and the dissipative trajectory when z=0.03, b=0.9 and K sub(d) =0.272313668. In the mode-locking phenomenon. we find that the generalized dimension D sub(-n) and superconverged $delta$ sub(n) are very close to D sub(-$infty$) =0.92403 and $delta$ sub($infty$) =2.16442 even for n～20 as listed in Table 1. In dissipative trajectory, the values of D sub(+n) and D sub(-n) for n～20 are estimated to be very close to D sub(+$infty$) =0.63267 and D sub(-$infty$) =1.89802 on the circle map. Thus, the values of the generalized dimension as nlongrightarrow$infty$ on dissipative Willbrink map are expected to be the same results as those for the circle map and to have the universal scaling exponents for a special scaling structure when the values of overbar(w), z, b, and k sub(d) have the different values.