The quasi-steady-state (tH > 10 τEoh) H mode with high plasma density (ELMy and ELM free) was routinely obtained by the injection of lower hybrid wave heating and lower hybrid current drive with a power threshold of 50 kW. The antenna spectrum was scanned over a wide range and τE was about 1.5-2.0 times that of the L mode scaling. The density increases by almost a factor of 3 during the H phase by gas puffing and the particle confinement time increases by more than this factor even with a line averaged density of 3 × 1013cm-3, which is about 60% of the Greenwald density limit. A hollow Te profile was achieved in the high density case. The experimental results reproducibly show a good agreement with the theoretical prediction for the LH off-axis power deposition profile. When a certain fraction of the plasma current is non-inductively sustained by the LH waves, a hollow current density profile is formed and the magnetic shear is reversed. This off-axis hollow profile and enhanced confinement improvement are attributed to a strong reduction of the electron thermal diffusivity in the reversed shear region.