This paper presents a diagnostic system, gamma-ray alpha-particle monitor (GRAM), for continuous monitoring of deuterium-tritium fusion alpha-particles in the MeV energy range escaped from the plasma to the first wall. The diagnostic is based on the detection of gamma-rays produced in nuclear reactions. The reactions Be-9(alpha,eta,gamma)C-12 and B-10(alpha,p,gamma)C-13 have been selected. For that purpose, Be- or B-10-target is placed on the first wall, where the alphas are expected to be mostly lost. Striking the target, the lost alphas generate specific gamma-rays, if their energy E-alpha > 1.5 MeV. To measure this gamma-ray emission, the target should be in the field of view of a collimated detector, which is protected from neutrons and background gammas. The calibrated detector could deliver absolute values of the lost alpha-particle flux with a temporal resolution depending on intensity of losses. A high-performance gamma-ray spectrometer with a novel architecture, GRITER, is proposed to be used in GRAM. It consists of a stack of the optically isolated high-Z fast scintillators with independent signal readout. GRITER is supposed to be operated at count-rates substantially exceeding the capability of a single crystal detector of the same size. The GRAM diagnostic system consists of two identical spectrometers, which measure both gamma-rays due to alpha-particle loss and gamma-ray background ensuring reliable data in a harsh reactor environment. GRAM could be tested during the non-DT plasma operation monitoring lost DD fusion products, neutral beam heating D-ions (E-D > 0.5 MeV) and ICRF accelerated H- and He-3-ions through the detection of gamma-rays resulting from nuclear reactions. The use of GRAM on JET and ITER, including events with extremely high loss rates, is discussed.