Abstarct: In the present study in context of one particle theory, amplification mechanism and efficiency of electron cyclotron maser instability are investigated primarely. Solving equations of motion for relativistic electrons numerically, the effects of magnetic field and electron beam energy on efficiency are studied. It is found that, in large signal regime for an electron beam by specific energy, there is an optimum magnetic field. The efficiency in this optimum magnetic field is maximized. In small signal regime, for a fixed of electron beam energy, increasing the magnetic field value increases the efficiency, but for a fixed magnetic field, increasing the beam energy decreases the efficiency. Then, applying kenitic theory, a stability analysis is carried out within the frxamework of the Vlasov-Maxwell equations with considering cylindrical waveguide and regardless of waveguide in the vacuum. Dispersion relation for electromagnetic perturbations has achieved in both cases.Numerical solving of dispersion relations provided precious information on wave propagation and the wavelengths resulting in wave amplifying.