We investigate the possible role of an accretion disk instability in p
roducing the giant outbursts seen in GRO J1744-28. Specifically, we st
udy the global, time-dependent evolution of the Lightman-Eardley insta
bility, which can develop near the inner edge of an accretion disk whe
n the radiation pressure becomes comparable to the gas pressure. Broad
ly speaking, our results are compatible with earlier works try Taam &
Lin and by Lasota & Pelat. The uniqueness of GRO J1744-28 appears to b
e associated with the constraint that, in order for outbursts to occur
, the rate of accretion at the inner edge must be within a narrow rang
e just above the critical accretion rate at which radiation pressure i
s beginning to become significant.