The Ignitor experiment is an advanced compact high magnetic field tokamak with cryogenically cooled (30 K) normal conductor magnets. Its main purpose is to produce deuterium-tritium plasma regimes where ignition can take place. From the neutronics point of view, the routine operations with 50% of tritium will lead to a very short (4 s) but intense emission of 14 MeV neutrons (up to 3×1019 n/s). The capability of the boron-free glass reinforced epoxy resin presently adopted for the insulation of the coils conductor to withstand the severe irradiation condition could be a key issue in the performance, reliability and lifespan of Ignitor. In order to better know the radiation environment in which the insulators will operate, calculations of the absorbed dose are performed using the parallelized version of MCNP-4B Monte Carlo code. A detailed 3D geometry description of the tokamak, an accurate representation of the neutron source distribution together with the more recent version of transport cross-section libraries EFF (European Fusion File) are used in this work. The variation of calculated dose depending on the insulator position inside the device, on the neutron energy spectra and on the total number of neutrons produced over the scheduled machine lifetime are discussed in the present paper.