A process for producing fuel by cracking a plastics-derived liquid, which is obtained from a pyrolysis process, using a dolomite catalyst. The plastics-derived liquid is produced by the pyrolysis of plastic waste, such as of one or more of polyethylene, polystyrene or polypropylene. The plastic-derived liquid is first subjected to a semi-batch catalytic cracking reaction over a very low cost dolomite catalyst to obtain high quality oil for fuel, which comprises mainly light and heavy naphtha. Moreover, the catalytic cracking reaction is conducted at operating temperatures lower than 320° C.