Gravitinos are very promising candidates for the cold dark matter of the Universe. Interestingly, to achieve a sufficiently long gravitino lifetime, R parity conservation is not required, thus preventing any dangerous cosmological influence of the next-to-lightest supersymmetric particle. When R parity is violated, gravitinos decay into photons and other particles with a lifetime much longer than the age of the Universe, producing a diffuse gamma-ray flux with a characteristic spectrum that could be measured in future experiments, such as GLAST or AMS-02. In this Letter we compute the energy spectrum of photons from gravitino decay and discuss its main qualitative features.