Increasing the density in a tokamak is limited by the so-called density limit, which is generally performed as an appearance of disruption causing loss of plasma confinement, or a degradation of high confinement mode which could further lead to a H → L transition. The L-mode and H-mode density limit has been investigated in EAST tokamak. Experimental results suggest that density limits could be triggered by either edge cooling or excessive central radiation. The L-mode density limit disruption is generally triggered by edge cooling, which leads to the current profile shrinkage and then destabilizes a 2/1 tearing mode, ultimately resulting in a disruption. The L-mode density limit scaling agrees well with the Greenwald limit in EAST. The observed H-mode density limit in EAST is an operational-space limit with a value of . High density H-mode heated by neutral beam injection (NBI) and lower hybrid current drive (LHCD) are analyzed, respectively. The constancy of the edge density gradients in H-mode indicates a critical limit caused perhaps by e.g. ballooning induced transport. The maximum density is accessed at the H → L transition which is generally caused by the excessive core radiation due to high Z impurities (Fe, Cu). Operating at a high density () is favorable for suppressing the beam shine through NBI. High density H-mode up to could be sustained by 2 MW 4.6 GHz LHCD alone, and its current drive efficiency is studied. Statistics show that good control of impurities and recycling facilitate high density operation. With careful control of these factors, high density up to 0.93 stable H-mode operation was carried out heated by 1.7 MW LHCD and 1.9 MW ion cyclotron resonance heating with supersonic molecular beam injection fueling.