  We report a 29Si-NMR study on the pressure-induced superconductivity (SC) in
an antiferromagnetic (AFM) heavy-fermion compound CeIrSi3 without inversion
symmetry. In the SC state at P=2.7-2.8 GPa, the temperature dependence of the
nuclear-spin lattice relaxation rate 1/T_1 below Tc exhibits a T^3 behavior
without any coherence peak just below Tc, revealing the presence of line nodes
in the SC gap. In the normal state, 1/T_1 follows a \sqrt{T}-like behavior,
suggesting that the SC emerges under the non-Fermi liquid state dominated by
AFM spin fluctuations enhanced around quantum critical point (QCP). The reason
why the maximum Tc in CeIrSi3 is relatively high among the Ce-based
heavy-fermion superconductors may be the existence of the strong AFM spin
fluctuations. We discuss the comparison with the other Ce-based heavy-fermion
superconductors.
