The problem of electron-ion temperature relaxation in beryllium plasma at various densities (0.185-18.5g/cm^{3}) and temperatures [(1.0-8)×10^{3} eV] is investigated by using the generalized Lenard-Balescu theory. We consider the correlation effects between electrons and ions via classical and quantum static local field corrections. The numerical results show that the electron-ion pair distribution function at the origin approaches the maximum when the electron-electron coupling parameter equals unity. The classical result of the Coulomb logarithm is in agreement with the quantum result in both the weak (Γ_{ee}<10^{-2}) and strong (Γ_{ee}>1) electron-electron coupling ranges, whereas it deviates from the quantum result at intermediate values of the coupling parameter (10^{-2}<Γ_{ee}<1). We find that with increasing density of Be, the Coulomb logarithm will decrease and the corresponding relaxation rate ν_{ie} will increase. In addition, a simple fitting law ν_{ie}/ν_{ie}^{(0)}=a(ρ_{Be}/ρ_{0})^{b} is determined, where ν_{ie}^{(0)} is the relaxation rate corresponding to the normal metal density of Be and ρ_{0}, a, and b are the fitting parameters related to the temperature and the degree of ionization 〈Z〉 of the system. Our results are expected to be useful for future inertial confinement fusion experiments involving Be plasma.