The magnetic interactions in beta-phase p-NPNN (p-nitrophenyl nitronyl nitroxide), a prototype genuine organic ferromagnet, have been studied by simultaneous measurements of magnetic heat capacity and susceptibility under hydrostatic pressures. A drastic reduction of the Curie temperature from 0.6 K at ambient pressure to 0.35 K at 7.2 kbar has been observed. This makes a significant contrast to the pressure-induced enhancement of the Neel temperature of organic antiferromagnets. A lowering of the magnetic lattice dimensionality is also observed at temperatures slightly above the Curie temperature under pressure, These observations are interpreted in terms of the virtual charge transfer mechanism.