The ferromagnetic to antiferromagnetic transition in genuine organic ferromagnets has been observed for the first time in the pressurized beta-phase p-nitrophenyl nitronyl nitroxide crystal at the pressure around p(c) = 6.5 +/- 0.5 kbar below 0.5 K, through the measurements of magnetic susceptibility and magnetization. The pressure dependence of the lattice parameters of its F2dd crystal structure, examined up to 12.6 kbar at room temperature, shows an anomaly near p(c). At ambient pressure, the effective intermolecular interaction is estimated to be (zJ) over tilde/k(B) = 2.3 K by the analysis of the magnetic heat capacity in the external field of 10 and 30 kOe. The Curie temperature in the ferromagnetic state at p < p(c) decreases with increasing pressure. Tn the antiferromagnetic state at p > p(c), however, the transition temperature starts to increase. The variation of intermolecular interactions under pressure, including their signs, is discussed on the basis of the charge-transfer mechanism and the recent ab initio method for the exchange interactions.