We present the first spectral observations obtained by Ginga of the low-mass X-ray binary source X1820-303 located in the globular cluster NGC 6624. Two two-component spectral models are found to provide good fits to the data: a bremsstrahlung component and a blackbody, or a power law with exponential cut-off and a blackbody. After considering the importance of Comptonization for the spectral and temporal behavior, the power law plus blackbody model is found to provide simple explanations for many of the observed features present in our data. By studying the variation in the amplitude of the 685-s binary period with source luminosity, it is possible to gain some insight into the source geometry. This reveals that our line of sight to X1820 - 303 is close to some 'critical' angle. Gravitationally induced shocks in the rim of the accretion disk may cause the height of the rim to vary with azimuthal angle, resulting in the quasi-sinusoidal X-ray orbital modulations.