This paper proposes a method for computing an airliner trajectory in its cruise phase, minimizing environmental impact. In particular, the problem of contrails is addressed. The proposed method is based on an algorithm derived from robotics, the Fast Marching Tree algorithm. After having been tested on Unmanned Aerial Vehicles (UAVs) and on computing trajectories in a wind field for commercial aircraft, it is now adapted to the case of contrails. Several modifications and additions are made to enable it to deal with soft obstacles that evolve over time, as well as the operational constraints associated with the cruise phase. The method is thus able to propose flight level changes in line with operational expectations, adaptable to the strategy of the user (airline for example). Two experiments are proposed on the Paris-Miami and Paris-Denver flights, showing low computation times and satisfactory results.