A neutron spectrometer was set-up by coupling a polyethylene converter with a monolithic silicon telescope, consisting of a DeltaE and an E stage-detector (about 2 and 500 microm thick, respectively). The detection system was irradiated with monoenergetic neutrons at INFN-Laboratori Nazionali di Legnaro (Legnaro, Italy). The maximum detectable energy, imposed by the thickness of the E stage, is about 8 MeV for the present detector. The scatter plots of the energy deposited in the two stages were acquired using two independent electronic chains. The distributions of the recoil-protons are well-discriminated from those due to secondary electrons for energies above 0.350 MeV. The experimental spectra of the recoil-protons were compared with the results of Monte Carlo simulations using the FLUKA code. An analytical model that takes into account the geometrical structure of the silicon telescope was developed, validated and implemented in an unfolding code. The capability of reproducing continuous neutron spectra was investigated by irradiating the detector with neutrons from a thick beryllium target bombarded with protons. The measured spectra were compared with data taken from the literature. Satisfactory agreement was found.