We examine the dependence of the morphology of spiral galaxies on the environment using the KIAS Value Added Galaxy Catalog (VAGC) which is derived from the Sloan Digital Sky Survey (SDSS) DR7. Our goal is to understand whether the local environment or global conditions dominate in determining the morphology of spiral galaxies. For the analysis, we conduct a morphological classification of galaxies in 20 X-ray selected Abell clusters up to z~0.06, using SDSS color images and the X-ray data from the Northern ROSAT All-Sky (NORAS) catalog. We analyze the distribution of arm classes along the clustercentric radius as well as that of Hubble types. To segregate the effect of local environment from the global environment, we compare the morphological distribution of galaxies in two X-lay luminosity groups, the low-$L_x$ clusters ($L_x$ < $0.15{ imes}10^{44}$erg/s) and high-$L_x$ clusters ($L_x$ > $1.8{ imes}10^{44}$erg/s). We find that the morphology-clustercentric relation prevails in the cluster environment although there is a brake near the cluster virial radius. The grand design arms comprise about 40% of the cluster spiral galaxies with a weak morphology-clustercentric radius relation for the arm classes, in the sense that flocculent galaxies tend to increase outward, regardless of the X-ray luminosity. From the cumulative radial distribution of cluster galaxies, we found that the low-$L_x$ clusters are fully virialized while the high-$L_x$ clusters are not.