The acceleration of LMXB 4U 1820-30 derived from its orbital-period derivative  was supposed to be the evidence for an Intermediate-mass black hole (IMBH) in the Galactic globular cluster (GC) NGC 6624. However, we find that the anomalous  is mainly due to the gravitational wave emission, rather than the acceleration in cluster potential. Using the standard structure models of GCs, we simulate acceleration distributions for pulsars in the central region of the cluster. By fitting the acceleration of J1823-3021A with the simulated distribution profiles (maximum values), it is suggested that an IMBH with mass  may reside in the cluster center. We further show that the second period derivative  of J1823-3021A is probably due to the gravitational perturbation of a nearby star.