A method is developed to compute the infrared signature behind a jet engine. The radiative transfer equation is solved with the Finite Volume Method (FVM) based on a double discretization of the spatial and the directional domain. Then, by solving step-by-step for different wave numbers for all directions, the value of the intensity received by a point placed at infinity looking at the computational domain with a defined angle and at a defined wave number is obtained. The resulting values of the intensity for a jet engine plume case compared very well with results from a validated ray-tracing model. A sensibility analysis has been carried out to assess the influence of the spatial and directional mesh, as well as the composition of the gas mixture on the results. The method appeared to be a very powerful and practical tool to study the spectral radiative signature created by a flow with arbitrary geometry.