We explore the non-standard mixing history of the five best solar twins in order to determine as precisely as possible their mass and age. For this, we computed a grid of evolutionary models with non-standard mixing at given metallicities with the Toulouse-Geneva code for a range of stellar masses assuming an error bar of about 50K in Teff. We choose the evolutionary model that best fit the observed low lithium abundances observed in the solar twins. Our best model for each solar twin provides a mass and age solution constrained by their Li content and Teff determination. Non- standard mixing is required to explain the low Li abundances observed in solar-twins. Li depletion due to the additional mixing in solar-twins is strongly mass dependent. An accurate lithium abundance measurement connected with non-standard models provides a more precise information about the age and mass better than that determined only by classical methods.