A simple model of the Fermi surface for an interpretation of the conduction electron spin resonance (CESR) results in Aluminium is developed. According to the real Aluminium Fermi surface 48 small rings with the large amount of the g-factor shift are arranged in five layers on the Fermi sphere, as distinct from the random distribution of them in the previous model proposed by Silsbee and Beuneu (SB). The present model reproduce known experimental CESR linewidth dependencies versus the frequency at different temperature region as well as the SB model. Additionally to the SB results the CESR linewidth is found to be independent from the magnetic field direction in the high temperature approximation. In both other cases (intermediate and low temperatures) the g-value anisotropy over Fermi surface is predicted to lead to the essential angular CESR linewidth dependence with five peaks. Some applications of the model to various systems with conduction electrons are discussed.