Law was born into a merchant family and became an East India Company writer in Bombay in 1715, graduating in 1720 to become a factor. In 1739 he was appointed Governor. He was recalled in 1742 following accusations of excessive expenditure in protecting the settlement from the Marathas. He retired to Broxbourne Manor, Broxbourne, England and became a Director of the Company for 1746–49, 1751–54 and 1756.