Cavity measurements of a high frequency (60 GHz) electron spin resonance (ESR) have been carried our for a single crystal of EuB6 at temperatures 4.2-50K in magnetic field up to 7 T, which has been aligned along  crystallographic direction. The influence of the experimental geometry on the parameters of the resonance line has been studied. It is found that in conditions of a homogeneous magnetic field the ESR spectrum in EuB6 is formed by a single resonance line at all temperatures including the ferromagnetic ordering region. The presence of the gradient of the magnetic field in the sample causes strong broadening of the resonance line at low temperatures and even may induce a double peak ESR structure. The analysis of the linewidth temperature dependence in EuB6 shows the anomalous growth of the line width below Curie temperature TC ~15 K.