Seawater desalination is vital to our modern civilization. Here, we report that the carbon honeycomb (CHC) has an outstanding water permeability and salt rejection in the seawater desalination, as revealed by molecular dynamics simulations. More than 92% of ions are rejected by CHC at applied pressures ranging from 50 to 250 MPa. CHC has a perfect salt rejection at pressures below 150Mpa.On increasing the applied pressure up to 150 MPa, the salt rejection reduces only to 92%. Pressure, temperature and temperature gradient are noted to play a significant role in modulating the water flux. The water flux increases with pressure and temperature. With the introduction of a temperature gradient of 3.5 K/nm, the seawater permeability increases by 33% as compared to room temperature. The water permeability of the carbon honeycomb is greater than other carbon materials and osmosis membranes including graphene (8.7 times) and graphyne (2.1 times). It indicates the significant potential of the carbon honeycomb for commercial application in water purification.