Hugh was the second and eldest surviving son of Richard Grosvenor, 2nd Marquess of Westminster and Lady Elizabeth Leveson-Gower. He became MP for Chester in 1847 and continued to represent that constituency until, on the death of his father in 1869 he succeeded as 3rd Marquess of Westminster and entered the House of Lords.
He opposed Gladstone's Reform Bill but following an improvement in their relationship he was created 1st Duke of Westminster in Gladstone's resignation honours in 1874. When Gladstone became Prime Minister again in 1880 he appointed Grosvenor as Master of the Horse. This was most appropriate as his interests lay in his estates, horse racing and country affairs.
He invested heavily in time and money in his estates in London and Cheshire, his principal home being Eaton Hall which he commissioned from Alfred Waterhouse in 1870. it has been described as "the most ambitious piece of Gothic Revival domestic architecture anywhere in the country".