A spin-glass is sensitive to an external magnetic field. An applied magnetic field dissolves degeneracy in the ground states of a spin-glass. The number of degeneracy is obtained as a function of the strength $H$ of an external magnetic field for the Edwards-Anderson model of a spinglass. Linear and nonlinear susceptibilities are studied at zero temperature. The nonlinear susceptibility ${\ensuremath{\chi}}_{2}$ defined by an expansion $m=\ensuremath{\chi}H+{\ensuremath{\chi}}_{2}{H}^{3}+\ensuremath{\cdots}$ for the magnetization $m$ is closely related to behavior of the local-field distribution around zero value. It is found, for the infinite-range limit of this model, that ${\ensuremath{\chi}}_{2}$ is a small positive quantity (0.04384) in contrast to the Sherrington-Kirkpatrick solution ($\ensuremath{-}\frac{1}{3\sqrt{2\ensuremath{\pi}}}=\ensuremath{-}0.13298$). The average ground-state energy is obtained for each applied magnetic field. Comparison with computer simulations is made for the infinite-range limit.