A new method to diagnose the degree of electron degeneracy in compressed fuel for fast-ignition inertial confinement fusion is proposed. We focus on 4.44-MeV -rays emitted in the reaction 9Be(,n)12C governed by fusion-produced energetic alpha-particles in a laser-imploded DT fuel pellet admixed with a small amount of 9B. In this case the compressed fuel pellet is not subjected to any heating laser pulse. We have evaluated the probability P-Be that the + 9Be reaction occurs during the slowing down of -particle. It is found that the reaction probability depends strongly on the degeneracy parameter , which is defined as the ratio of electron temperature to the Fermi energy. We show the possibility of diagnosing the electron degeneracy from the P-Be - diagram by detecting the 4.44-MeV -quanta and DT neutrons emitted from the dense core plasma.