The novel one-particle Monte Carlo procedure for the simulation of the longitudinal optical phonon distribution accumulation generated by electrons in a high electric field is presented in detail. The phonon and electron distributions are obtained employing novel code in zinc-blend n-type GaN crystals. The main quality of this code is the avoidance of the short-time-step procedure appropriate to the conventional ensemble Monte Carlo method. The maximum value of the phonon distribution function dramatically exceeds the thermal-equilibrium one. The influence of the phonon accumulation on the electron kinetic characteristics of zinc-blend GaN and other features, such as longitudinal optical phonon number inversion with respect to acoustic phonon modes, are discussed.