Eighteenth-century sources disagree about many details of his life, and consequently his early life is shrouded in uncertainty. He was probably born in Glasgow, the child of the violinist Duncan McGibbon and his wife Sarah Muir, although earlier sources say he was born in Edinburgh. He may have studied in London under William Corbett, and may have travelled in Italy in his youth, possibly with Corbett. He seems to have settled in Edinburgh in the 1720s.
Although a prolific composer, particularly for the flute, recorder and fiddle, only a few of his works are now known. Grove says they "vary in quality"; his early work shows influences of Corelli, Handel, Veracini, and Purcell, while after 1740 he produced many settings of Scottish tunes, which were then very popular, but still show an Italian influence.