We present 12CO (2-1) data of three Virgo spirals-NGC 4330, NGC 4402 and NGC 4522 obtained using the Submillimeter Array. These three galaxies show clear evidence of ram pressure stripping due to the cluster medium as found in previous H I imaging studies. Using the high-resolution CO data, we investigate how the properties of the inner molecular gas disc change while a galaxy is undergoing H I stripping in the cluster. At given sensitivity limits, we do not find any clear signs of molecular gas stripping. However, both its morphology and kinematics appear to be quite disturbed as those of H I. Morphological peculiarities present in the molecular and atomic gas are closely related with each other, suggesting that the molecular gas can be also affected by strong intracluster medium (ICM) pressure even if it is not stripped. CO is found to be modestly enhanced along the upstream sides in these galaxies, which may change the local star formation activity in the disc. Indeed, the distribution of Hα emission, a tracer of recent star formation, well coincides with that of the molecular gas, revealing enhancements near the local CO peak or along the CO compression. FUV and Hα share some properties in common, but FUV is always more extended than CO/Hα in the three galaxies, implying that the star-forming disc is rapidly shrinking as the molecular gas properties have changed. We discuss how ICM pressure affects dense molecular gas and hence star formation properties while diffuse atomic gas is being removed from a galaxy.