Under increasing pressure, the Ne?el temperature of the heavy-fermion compound Ce7Ni3 (TN=1.9 K for P=O) decreases and vanishes near Pc≈0.33 GPa. Non-Fermi-liquid behavior appears at 0.4 GPa in both the specific heat and ac magnetic susceptibilitiy, Cm /T∼ - lnT and χac∝(1 - αT1/2). Above 0.62 GPa, the normal Fermi-liquid state recovers, as indicated by the T independence of CmT and the T2 dependence of the magnetic resistivity. The observed crossover with pressure is described by self-consistent renormalization theory of spin fluctuations (SF) in terms of the characteristic SF temperature T0 which increases by a factor of 20 for 0.33≤P≤0.75 GPa.