The ultracompact low-mass X-ray binary 4U 1820-30 situated in the globular cluster NGC 6624 has an orbital period of only approximate to 11.4 min, which likely implies a white dwarf companion. The observed X-ray bursts demonstrate a photospheric radius expansion phase and therefore are believed to reach the Eddington luminosity, allowing us to estimate the mass and the radius of the neutron star (NS) in this binary. Here, we re-analyse all Rossi X-ray Timing Explorer observations of the system and confirm that almost all the bursts took place during the hard persistent state of the system. This allows us to use the recently developed direct cooling tail method to estimate the NS mass and radius. However, because of the very short, about a second, duration of the cooling tail phases that can be described by the theoretical atmosphere models, the obtained constraints on the NS radius are not very strict. Assuming a pure helium NS atmosphere, we found that the NS radius is in the range 10-12 km, if the NS mass is below 1.7 M-circle dot, and in a wider range of 8-12 km for a higher 1.7-2.0 M-circle dot NS mass. The method also constrains the distance to the system to be 6.5 +/- 0.5 kpc, which is consistent with the distance to the cluster. For the solar composition atmosphere, the NS parameters are in strong contradiction with the generally accepted range of possible NS masses and radii.