Spectral unmixing of hyperspectral images consists of estimating pure material spectra with their corresponding proportions (or abundances). Non-linear modelisation of spectral unmixing problem is of very recent interest within the signal and image processing community. This letter proposes a new non-linear unmixing approach using Fan bilinear-bilinear model and non-negative matrix factorization method that takes into account physical constraints on spectra (positivity) and abundances (positivity and sum-to-one). The proposed method is tested using a projected Gradient algorithm on synthetic and real data. The performances of this method are compared to linear approach and to recent non-linear approach.