We have performed an On-The-Fly (OTF) mapping survey of 12CO(J = 1-0) emission in 28 Virgo cluster spiral galaxies using the Five College Radio Astronomy Observatory (FCRAO) 14 m telescope. This survey aims to characterize the CO distribution, kinematics, and luminosity of a large sample of galaxies covering the full extents of stellar disks, rather than sampling only the inner disks or the major axis as was done by many previous single dish and interferometric CO surveys. CO emission is detected in 20 galaxies among the 28 Virgo spirals observed. An atlas consisting of global measures, radial measures, and maps is presented for each detected galaxy. A note summarizing the CO data is also presented along with relevant information from the literature. The CO properties derived from our OTF observations are presented and compared with the results from the FCRAO Extragalactic CO Survey by Young et al. which utilized position-switching observations along the major axis and a model fitting method. We find that our OTF-derived CO properties agree well with the Young et al. results in many cases, but the Young et al. measurements are larger by a factor of 1.4-2.4 for seven (out of 18) cases. We will explore further the possible causes for the discrepancy in the analysis paper currently under preparation.