This research is focused on the development of a one-dimensional mathematical model (with respect to the height of the reactor) of fluidized bed gasifier in a bubbling regime at atmospheric pressure, by means of simulation by numerical methods with the use of MATLAB, based on the Theory of the Two Phases (emulsion and bubble). The model developed through empirical equations proposed in several publications, allows the prediction of the energy quality (LHV) and the composition of the synthesis gas throughout the height of the reactor during the gasification process, by estimating the molar flows of the main volatile species produced (CO, CO2, H2O, H2, O2, CH4, N2 and char). In addition, the model has been validated with research using the values of the molar fractions of hydrogen (H2), carbon monoxide (CO) and methane (CH4) obtained experimentally.