We present preliminary results on the diffractive charmonium production at the HERA-B experiment. An excess of the events with a large rapidity gap between J/\psi and the outgoing proton system is observed, while a much smaller excess of that between J/\psi and the outgoing nucleus system is found. The A-dependence for the events with the large rapidity gap is measured. The search for the Double Pomeron Exchange charmonium production results in the upper limits on the proton--carbon cross-section times the radiative branching fraction of \sigma _{\chi c0}^DPE \times {BR } < 0.5nb and \sigma _{\chi c1,2}^DPE \times {BR } < 1.1nb at 90\% C.L. The upper limits cover part of the region of the theoretical expectations.

PACS numbers: 13.85.Hd, 25.40.Ep