To investigate the intrinsic nature of spin correlations in La-214 high-T c cuprate, we performed neutron scattering measurement on La 1.94-x Sr x Ce 0.06CuO 4 (LSCCO) samples for two different hole concentrations. Since the Ce-doping reduces the hole concentration without changing the bulk lattice distortion, the corrugation of CuO 2 planes in the Sr and Ce co-doped LSCCO system is more relaxed compared with that in La 2-x Sr x CuO 4 (LSCO) at equivalent hole concentration. In the optimally doped x=0.18 sample, clear spin gap structure was observed, as is the case of the optimally doped LSCO. Therefore, the spin gap structure is insensitive to the lattice distortion. In the underdoped x=0.14 sample, the local spin susceptibility (χ″(ω)) above 2 meV increases with increasing the energy transfer (ω) and reaches an intensity maximum at ∼7 meV, exhibiting a gap-like structure. The observation of gap-like structure in the present underdoped sample is quite different from the energy-independent χ″(ω) reported for underdoped LSCO. The possible origin of difference of spin excitations is discussed from the viewpoint of two-component picture for spin fluctuations.