<p>This work investigates relativistic electron radiation in a gyro-klystron device, incorporating the effect of beam energy spread and initial perpendicular velocity component. In an optical klystron a drift or dispersion section separates two undulator sections of identical length. Similarly, a dispersion section separates two solenoids of identical length in the gyro-klystron.</p><p>Based on the cyclotron maser interaction concept, the gyro-klystron produces radiation at the cyclotron resonance frequency when an electron performs helical motion in the first solenoid. The influence of the initial perpendicular velocity component on spectral properties of gyro-klystron is shown in the paper. Findings demonstrate the importance of maintaining a low energy spread parameter to ensure efficient beam–wave interaction. The study shows an effective <b>inverse relationship between energy spread and spectral gain of gyro-klystron,</b> the effect of increasing initial perpendicular velocity component consistently enhances <b>gain and intensity</b> across all values of energy spread parameter. As a result, higher <b>perpendicular velocity values</b> mitigate the beam quality requirements while broadening the operational range of the gyro-klystron. It is also reveals that dispersion strength increases, <b>phase coherence improves</b>, and the <b>spectral bandwidth narrows</b>, indicating stronger resonance. An analytical treatment has been applied for the formulation of the gain expression.</p>