A process for continuously eliminating mercury and mercury compounds in liquid hydrocarbons for example, a natural gas condensate comprising: (a) bringing liquid hydrocarbons containing mercury and mercury compounds, as well as asphaltene into contact, in a first adsorption treatment zone, with a porous inorganic adsorbent which is at least one of materials selected from the group consisting of activated carbon, activated clay, alumina, silica gel, silica-alumina and zeolite, and then (b) bringing the liquid hydrocarbons from the adsorption treatment zone alter the adsorption treatment into contact, in a second adsorption treatment zone, with an activated carbon having a specific surface area from 200 m²/g to 2500 m²/g and an average pore diameter from 10 Å to 100 Å. Mercury and mercury compounds in liquid hydrocarbons containing a great amount of heavy ingredients such as asphaltene can be eliminated continuously for a long period of time.