We present high-resolution ($1\farcs8$ -- $4\farcs5$) CO data of the Virgo spiral galaxy NGC 4569, obtained using the Nobeyama Millimeter Array. We found that the molecular gas is highly concentrated in the circumnuclear region with two off-center peaks. A CO image with the highest angular resolution of $2\farcs0 \times 1\farcs8$ shows that six blobs likely form a circumnuclear elliptical ring (CER) with a semi-major axis radius of 720 pc. The CER shows a strongly twisted velocity field, and the position--velocity (PV) diagram shows significant forbidden velocity components. These kinetic features are understood as being non-circular motion due to a bar-potential. We found that the CER coincides with the H$\alpha$ bright central core and th...