We investigate the possible role of an accretion disk instability in producing the giant outbursts seen in GRO J1744-28. Specifically, we study the global, time dependent evolution of the Lightman-Eardley instability which can develop near the inner edge of an accretion disk when the radiation pressure becomes comparable to the gas pressure. Broadly speaking, our results are compatible with earlier works by Taam \& Lin and by Lasota \& Pelat. The uniqueness of GRO J1744-28 appears to be

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... ed with the constraint that, in order for outbursts to occur, the rate of accretion at the inner edge must be within a narrow range just above the critical accretion rate at which radiation pressure is beginning to become significant.