In partnership with his cousin Richard Trevithick, the inventor of the "high pressure" steam engine, and the entrepreneur Davis Giddy, Vivian financed the production of the first steam carriage and was granted a joint patent for high pressure engines for stationary and locomotive use in March 1802.
His first wife was Sarah Carbis.
His second wife was Frances Knight dau of Stephen Knight of Illogan
In 1801 Trevithick completed his first full-sized road locomotive in Camborne, demonstrating it to the public on Christmas Eve with Vivian at the controls. The first day it ran about the streets and up the very steep Beacon Hill. The next day it went down to the village of Crane so that Vivian's family, who lived there, might see it. In a further trial, one week later, the machine overturned in a rut. It was dragged into a shed while Trevithick and Vivian had lunch at a nearby inn; on their return the boiler had run dry, setting fire to the machine's timber frame.
A second locomotive was tried in Camborne and, at the beginning of 1803, in London. It was shipped to London in the Little Catherine, a temporary packet commanded by John Vivian (1784–1871), nephew of Andrew Vivian. In August 1803, Mr. Felton, of Leather Lane, London, was paid for building the coachwork. William West assembled the machine, under the supervision of Trevithick and Vivian. It ran successfully, although receiving surprisingly little lasting public attention, but again the state of the road surfaces of the time put paid to the enterprise: the carriage was put out of action with a twisted frame. In the face of this setback Vivian withdrew from the partnership.