Helioseimic investigation shows that convective overshooting can penetrate 0.37HP to the location where the temperature is 2.5 × 106 K, which is the typical temperature of the reaction Li7(p, α)He4. This indicates that overshooting mixing should be involved in investigating the solar Li abundance problem. Observations of the Li abundance of solar twins show that the Sun is not very peculiar. Overshooting mixing should also be involved in investigating Li abundance in clusters. However, fully overshooting mixing with a length of 0.37HP results in too much Li depletion to fit the observations in the solar case. Therefore, using the diffusive process to describe the overshooting is more suitable. The diffusive overshooting approach requires the turbulent root-mean-square velocity in the overshooting region in order to calculate the diffusion coefficient. Turbulent convection models (TCMs), which are suggested by helioseimic investigation, can provide the turbulent properties in the overshooting region. However, TCMs are often too complex to be applied in calculations of stellar evolution. There is an easier way to use the asymptotic solution of TCMs. In this paper the asymptotic solution of Li & Yang's TCM, which results in agreement in both solar sound speed and solar Li abundance, is used to investigate the Li abundance in clusters (Hyades, Praesepe, NGC 6633, NGC 752, NGC 3680 and M67). It is found that overshooting mixing leads to significant Li depletion in old clusters (t > 1 Gyr) and has little effect in young clusters (t < 1 Gyr).