Swelling in fiber-reinforced composites is anisotropic. In this work, dealing with glass fiber epoxy composite immersed in distilled water, swelling coefficients are obtained in each direction experimentally. Swelling behaviour in the fiber direction was constrained by the non-swelling fibers and was close to null, while swelling in the transverse directions was found to occur freely—similar to the unconstrained polymer. An analytical method for predicting anisotropic swelling in composites from the swelling of the matrix polymer is reported in this work. The method has an advantage that it is simple to use in practice and requires only a swelling coefficient of the matrix polymer, elastic constants of the matrix and fibers, and a known fiber volume fraction of the composite. The method was validated using finite element analysis. Good agreement was obtained and is reported between experimental hygroscopic swelling data, analytical and numerical results for composite laminates, indicating the validity of this predictive approach.