The pressure dependence of transport properties in CeRhIn5 was studied up t
o 8.5 GPa by using a diamond-anvil cell. The electrical resistivity does no
t follow the T-2-dependecne of a Fermi liquid nature under any pressure. In
this non-Fermi liquid state, superconductivity was observed in a wide pres
sure range of 1.5 GPa < P < 7.6 GPa. The superconducting temperature TC has
a double-maximum structure with a minimum at 5.2 GPa. A maximum of T-C = 2
.2 K was observed at P = 2.5 GPa, where the corresponding electrical resist
ivity just above TC has the maximum. The upper critical field H-C2 and the
magnetoresistances were also investigated under pressure.