  We have carried out high pressure experiment on the pressure-induced
superconductor CeIrSi$_3$ without inversion center. The electrical resistivity
and ac heat capacity were measured in the same run for the same sample. The
critical pressure of the antiferromagnetic state was determined to be $P_{\rm
c}$ = 2.25 GPa. The heat capacity $C_{\rm ac}$ shows both antiferromagnetic and
superconducting transitions at pressures close to $P_{\rm c}$. The
superconducting transition temperature $T_{\rm sc}$ shows a maximum value of
1.6 K around $2.5-2.7$ GPa. At 2.58 GPa, a large heat capacity anomaly was
observed at $T_{\rm sc}$ = 1.59 K. The jump of the heat capacity in the form of
${\Delta}{C_{\rm ac}}/C_{\rm ac}(T_{\rm sc})$ is 5.7 $\pm$ 0.1. This is the
largest value observed among all superconductors studied previously, suggesting
the strong-coupling superconductivity in CeIrSi$_3$. The large magnitude and
anisotropy of the upper critical field $B_{\rm c2}$ at 2.65 GPa is discussed
from view points of the strong-coupling superconductivity and the reduced
paramagnetic effect in the non-centrosymmetric superconductor. Above $P_{\rm
c}$, the electrical resistivity shows the anomalous $T$-linear dependence in
the wide temperature region from $T_{\rm sc}$ to 30 K, which is different from
the Fermi liquid theory. Meanwhile, the heat capacity $C_{\rm ac}/T$ shows a
simple temperature dependence in the normal state above $T_{\rm sc}$. These
features do not seem to be explained simply by the spin fluctuation theory. The
electronic specific heat coefficient at $T_{\rm sc}$ is approximately unchanged
as a function of pressure, even at $P_{\rm c}$.
