The g factor of Li-like ions in the range Z = 6-92 is evaluated. The interelectronic-interaction corrections of order 1/Z² and higher are taken into account by the configuration-interaction Dirac-Fock method. This result is combined with the 1/Z term derived within a rigorous QED approach. The one-electron QED correction of first order in α is obtained by employing our recent results for the self-energy term and by evaluating the vacuum-polarization term. The screening of the QED effects is calculated to the leading orders in αZ and 1/Z. A significant improvement of the theoretical accuracy of the g-factor values is achieved.