He moved to Michigan in 1837 and worked as a clerk with his brother for two years in Albion. He was also a clerk in the state commissioner’s office in Monroe from 1839-1840, and a clerk in Jonesville from 1840-1844. In 1840, he became a charter member of the Odd Fellows in Jonesville and passed all the chairs of that Order. On February 25, 1844 he married Sally Ann Champlin in Stillwater, New York and they had four children together. After returning to Michigan he became a merchant at Jonesville. In 1854, he established the banking house of Grosvenor & Co., in which he was president and manager. In 1855, he joined the Freemasons and achieved the rank of Master Mason. He also regularly attended the Presbyterian Church.
In 1864, Grosvenor was elected to the office of Lieutenant Governor of Michigan and served during Governor Henry H. Crapo’s first term from 1865-67. He was then appointed State Treasurer of Michigan from 1867-71 during Crapo’s second term and Henry P. Baldwin’s first term.
Grosvenor served a member and president of the board of state building commissioners from 1871-1879. He then served on the board of regents at the University of Michigan from 1879-88. He was also long vice president of the Jackson & Fort Wayne railroad company and a director of some insurance companies and other corporations. In 1903, he became a member of the Michigan Republican State Central Committee.