In this paper, the effect of the ITER stray magnetic field (SMF) on the operation of the European gyrotron has been studied. The SMFs include the magnetic field generated by neighboring gyrotrons, the ITER tokamak, and also the field perturbations caused by the ferromagnetic structural materials used in the ECRH building. The 3-D self-consistent electrostatic code ARIADNE has been used for the evaluation of the SMF effect on the electron beam in the cavity and the collector region. It is shown that the beam parameters at the cavity of the gyrotron are not significantly affected by the SMF. On the other hand, the magnetic field lines in the collector region are significantly deformed in the presence of the SMF. A part of the electron beam is guided to the inappropriately cooled part of the collector surface, while the electron beam power is distributed in a significantly smaller area of the collector walls. In addition, the use of an advanced transverse sweeping system is proposed which would allow to compensate the SMF and to improve the collector operation.