Wind generation increase in electric power systems is a general trend in many countries. Variable speed wind turbines (WT) with doubly fed induction generators (DFIG) are commonly used for this purpose. In order to ensure stability and obtain the desired performance when WT are subject to transient disturbances, their control system needs to operate properly. This work aims at tuning the controllers comprising the DFIG control structure enhancing transient performance during electric faults and so contributing to the Low-Voltage Ride-Through (LVRT) capability. To do this, a multi-objective particle swarm optimization algorithm (MOPSO) is proposed applying to the complete dynamic model of the WT (electrical and mechanic parts) and minimizing a set of objective functions (OF) adapted to the electrical network fault problem. Tuning performance is compared with the classical symmetrical optimum method. Simulation results show that the MOPSO and penalization of both electrical and mechanical variables in the OF led to improved mechanical oscillations damping and voltage performance during a fault event, enhancing the LVRT capability even for the more critical condition of the flexible mechanical coupling. The results validate the proposed MOPSO as an effective tool capable of improving the behavior of this type of control for WT.