The helioseimic investigation shows that the convective overshooting can penetrate 0.37 H _ { P } to the location where the temperature is 2.5 \times 10 ^ { 6 } K which is the typical temperature of the reaction Li ^ { 7 } ( p, \alpha ) He ^ { 4 } .
This indicates that the overshooting mixing should be involved in investigating the solar Li abundance problem .
Observations of Li abundance of solar-twins show that the sun is not very peculiar .
The overshooting mixing should be also involved in investigating Li abundance in clusters .
However , the fully overshooting mixing with the length of 0.37 H _ { P } results in too much Li depletion to fit the observation in the solar case .
Therefore , using the diffusive process to describe the overshooting is more suitable .
The diffusive overshooting approach requires the turbulent r.m.s .
velocity in the overshooting region 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 the calculations of the stellar evolution .
It is an easier way to use the asymptotic solution of TCMs .
In this paper , I use the asymptotic solution of Li & Yang ’ s TCM , which results in agreements in both solar sound speed and solar Li abundance , to investigate Li abundance in clusters ( Hyades , Praesepe , NGC6633 , NGC752 , NGC3680 & M67 ) .
It is found that the overshooting mixing leads to significant Li depletion in the old clusters ( t > 1 Gyr ) and little effect in the young clusters ( t < 1 Gyr ) .