A new model of chlorophyll a fluorescence emission by plant leaves, FluorMODleaf, is presented. It is an extension of PROSPECT, a widely used leaf optical properties model that regards the leaf as a pile of N absorbing and diffusing elementary plates. In FluorMODleaf, fluorescence emission of an infinitesimal layer of thickness dx is integrated over the entire elementary plate. The fluorescence source function is based on the excitation spectrum of diluted isolated thylakoids and on the emission spectra of isolated photosystems, PSI and PSII, which are the main pigment-protein complexes involved in the initial stages of photosynthesis. Scattering within the leaf is produced by multiple reflections within and between elementary plates. The input variables of FluorMODleaf are: the number of elementary plates N, also called leaf structure parameter, the total chlorophyll content Cab, the total carotenoid content Ccx, the equivalent water thickness Cw, and the dry matter content Cm (or leaf mass per area), as in the new PROSPECT-5, plus the σII/σI ratio referring to the relative absorption cross section of PSI and PSII, and the fluorescence quantum efficiency of PSI and PSII, τI and τII, that are introduced here as mean fluorescence lifetimes. The model, which considers the reabsorption of emitted light within the leaf, allows good quantitative estimation of both upward and downward apparent spectral fluorescence yield (ASFY) at different excitation wavelengths from 400 nm to 700 nm. It also emphasizes the role of scattering in fluorescence emission by leaves having high chlorophyll content.