Liam Brace, aged 24, of North Road, Thornbury, was found with 5.4 microgrammes of delta-9-tetrahydrocannabinol (cannabis) per litre of blood in his system on January 23.
The limit is two microgrammes per litre of blood.
Brace pleaded guilty to drug-driving at Bristol Magistrates Court on Tuesday, July 8.
He was banned from driving for 12 months, fined £276 and must also pay £85 in costs plus a £110 surcharge – a total of £471.