A novel stochastic model to produce voiced sounds is proposed and, mainly, the corresponding identification of some model parameters using an Artificial Neural Network (ANN). The procedure described in this paper is about an intermediate step, which has as final objective to identify pathologies in the vocal folds through the voice of patients, that is, through a non-invasive method. The proposed model presented here uses the source-filter Fant theory and three main novelties are presented: a new mathematical model to produce voice obtained from the unification of two other deterministic one mass-spring-damper models obtained from the literature; a stochastic model that can generate and control the level of jitter resulting even in hoarse voice signals and/or with pathological characteristics but using a simpler model than those usually discussed in the literature; and the most important novelty, the identification of parameters of the proposed model, from experimental voice signals, using an ANN, particularly in a pathological case. The proposed neural network-based identification method requires a construction of a database from which an ANN can be trained to learn the nonlinear relationship between the parameters of the stochastic model and some relevant quantities of interest. The corresponding inverse stochastic problem is then solved in two cases: for one utterance corresponding to a normal voice and for another utterance corresponding to a pathological case corresponding to a nodulus in the vocal folds, helping to validate the model.