The invention provides an activated carbon supported cobalt based catalyst for directly converting of synthesis gas to mixed linear alpha-alcohols and paraffins, comprising cobalt, an activated carbon carrier, a metal promoter which is at least one selected from the group consisting of a zirconium component, a lanthanum component, a cerium component, a chromium component, a vanadium component, a titanium component, a manganese component, a rhenium component, a potassium component, a ruthenium component, a magnesium component and a mixture thereof, wherein the cobalt and the promoter are deposited on the activated carbon carrier or substantially uniformly dispersed therein, and the metal promoter is present in the form of a metal, an oxide or a combination thereof.