Being able to predict the different transitions of vegetation mosaics in humid environments is one of the main objectives in the study of vegetation dynamics. This work attempts to model the capacity of the forest in humid tropical ecosystems, to replace grassland in landscape mosaics if no appropriate management plan is implemented. We build in one spatial dimension, a reaction-dispersion model with nonlocal dispersion and we study the long-term dynamics of forest-grassland mosaic by the mean of the traveling wave solution setting. Precisely, we prove the existence of a traveling wave that connects the forest homogeneous steady state to the grassland homogeneous steady state. We also characterise the minimal wave speed of the aforementioned forest-grassland traveling wave. Moreover, we provide numerical simulations that depict how some parameters of the model may shape variations of the minimal speed.