The out-of-plane resistivity (rho(c)) has been measured in under-doped La2-xSrxCuO4 under pressure to investigate the nature of the superconducting transition. The antiferromagnetic insulating sample with x 0.020 did not show superconductivity even under pressure. However, in the non-superconducting samples with x 0.035 and 0.045, an appreciable but incomplete drop of rho(c) was observed with lowering temperature and increasing pressure. The drop of rho(c) under pressure suggests the existence of the intrinsic phase separation or inhomogeneity around x similar to 0.05: (C) 2003 Elsevier B.V. All rights reserved.