  It is generally thought that an ultracompact X-ray binary is composed with a
neutron star and a helium white dwarf donor star. As one of the most compact
binaries, 4U 1820-303 in globular cluster NGC 6624 was predicted an
orbital-period derivative at a rate of $\dot{P}/P\sim1.1\times10^{-7}$ ${\rm
yr^{-1}}$ if the mass transfer is fully driven by gravitational radiation.
However, the recent analysis of the 16 ${\rm yr}$ data from \textit{Rossi X-ray
Timing Explorer} and other historical records yielded a negative orbital-period
derivative in the past $35$ yr. In this work, we propose an evolutionary
circumbinary (CB) disk model to account for this anomalous orbital-period
derivative. 4U 1820-30 was known to undergo superbust events caused by runaway
thermal nuclear burning on the neutron star. We assume that for a small
fraction of the superbursts, part of the ejected material may form a CB disk
around the binary. If the recurrence time of such superbursts is $\sim10,000$
yr and $\sim10$% of the ejected mass feeds a CB disk, the abrupt
angular-momentum loss causes a temporary orbital shrink, and the donor's radius
and its Roche-lobe radius do not keep in step. Driven by mass transfer and
angular-momentum loss, the binary would adjust its orbital parameters to
recover a new stable stage. Based on the theoretical analysis and numerical
simulation, we find that the required feed mass at the CB disk is approximately
$\sim 10^{-8}$ ${\rm M_{\odot}}$.
