The Green's-function technique is used to obtain, for the first time, the parallel and perpendicular susceptibilities (${\ensuremath{\chi}}_{\ensuremath{\parallel}}$ and ${\ensuremath{\chi}}_{\ensuremath{\perp}}$) for an antiferromagnetic crystal with the associated spins forming the type 3a fcc structure which gives rise to a four-sublattice model. The technique involves the random-phase approximation for the decoupling scheme. The mathematics involved in the procedure for ${\ensuremath{\chi}}_{\ensuremath{\parallel}}$ is much more tedious and lengthy. The functional dependence of ${\ensuremath{\chi}}_{\ensuremath{\parallel}}$ on temperature ($T$) is obtained for $Tl{T}_{N}$ as well as $Tg{T}_{N}$. The analytic expression for the N\'eel temperature ${T}_{N}$ is already known from Lines's work. ${\ensuremath{\chi}}_{\ensuremath{\parallel}}$ reduces to zero at $T=0$. The limiting value of ${\ensuremath{\chi}}_{\ensuremath{\parallel}}$ at $T={T}_{N}$ is also evaluated. The procedure for the perpendicular susceptibility, ${\ensuremath{\chi}}_{\ensuremath{\perp}}$, is based on some drastic approximations which are applicable only when $T$ is close to absolute zero. In particular, the limiting value of ${\ensuremath{\chi}}_{\ensuremath{\perp}}$ at $T=0$ is exact. The present results, for the four-sublattice model, may be compared with the corresponding results for the simple two-sublattice model as obtained by Lines. The spin-spin correlation functions evaluated in an intermediate step of the procedure are very important and may be useful in the investigation of other spin-related properties of the model.