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 plus a blackbody, or a power law with exponential cut-off plus a blackbody. In both cases, inclusion of an iron line at 6.7 keV improves the fits. After considering the importance of Comptonization for the spectral and temporal behaviour, we select the power law plus blackbody model. This model then provides simple explanations for many of the observed features present in our data. The model requires a scattering cloud surrounding the neutron star, with a Thomson optical depth of approximately 7.