To date, to simulate biodiesel production, kinetic models from different authors have been provided, each one usually applied to the use of a specific vegetable oil and experimental conditions. Models, which may include esterification, besides transesterification simulation, were validated with their own experimental conditions and raw material. Moreover, information about the intermediate reaction steps, besides catalyst concentration variation, is either rare or nonexistent. Here, in this work, a universal mathematical model comprising the chemical kinetics of a two-step (esterification and transesterification) vegetable oil-based biodiesel reaction is proposed. The proposed model is universal, as it may simulate any vegetable oil biodiesel reaction from the literature. For this purpose, a mathematical model using the software MATLAB has been designed. Using the mathematical model, the estimation of mass variation with time, of both reactants and products, as well as glyceride conversion and homogeneous catalyst concentration variation (instead of only alcohol/catalyst solution) are allowed. Moreover, analysis of the influence of some important variables affecting the reaction kinetics of biodiesel production (e.g., catalyst concentration), along with comparison and model validation with data from different authors may be carried out. In addition, Supplementary material with a collection of 290 rate constants, derived from 55 different experiments using different vegetable oils and conditions is provided.