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The influence of the Lode parameter on ductile failure has been pointed out by different authors even at high triaxiality stress states. However, one of the most widely used model for ductile damage, like the Gurson-Tvergaard (GT) model, systematically disregard the role played by the third stress invariant. In this paper, an improvement of the classical Gurson-Tvergaard model is proposed. The new relation takes into account the effect of triaxiality and Lode parameter through the q(1) and q(2) GT parameters. The convexity of the proposed yield surface has been examined and ensured. The integration of the new constitutive equations as well as the consistent tangent modulus have been formulated and implemented in a Finite Element code. A computational 3D cell has been used to prescribe both macroscopic triaxiality and Lode parameter during loading. Numerical simulations are presented for Weldox 960 steel with different initial porosities and for different prescribed macroscopic triaxialities and Lode parameters using a computational 3D cell methodology. The results are compared with those obtained with a J(2) voided cell. These comparisons show that the improved model captures adequately the Lode effect on the stress-strain curves and on the void growth. (C) 2015 Elsevier Masson SAS. All rights reserved.