For improved actions composed of plaquette and rectangular six-link loops, η, the ratio of renormalized to bare anisotropies, is calculated for ξ=2, 3, 4, and 6 in the β region where numerical simulations such as hadron spectroscopy are currently carried out. The β dependence of η for the renormalization-group-improved actions is quite different from those of the standard and Symanzik actions. In the Iwasaki and DBW2 (doubly blocked from Wilson action in two-coupling space) actions, η remains almost constant in a wide range of β, which is also different from the one-loop perturbative results, while in the case of the Symanzik action, η increases as β decreases, which is qualitatively similar to the perturbative result, but the slope is steeper. In the calculation of η close to and in the confined phase, we have applied a link integration method to suppress the fluctuation of the gauge field. Some technical details of the integration method are summarized.