After a brief stay in Madras, he was assigned as a Civil Surgeon to Tenasserim, Burma, where he studied local plants and made collecting trips to the Barak River valley in Assam.
He received the Linnaean Gold Medal of the Society of Apothecaries in 1830 (botanical class) and joined the East India Company as an assistant surgeon at Madras on 24 September 1832.
When Nathaniel Wallich visited South Africa, he was made in-charge of the Calcutta Botanical Garden and also acted as Professor of Botany at the Medical College from 1842 to 1844.
The Calcutta Journal of Natural History, produced with assistance from him ceased and the subscriptions were used by John McClelland to publish Griffith's unpublished manuscripts.
[2] He married Emily Henderson (sister of his brother's wife) in September 1844 and in December of the same year he sailed from Calcutta to Malacca but on arrival in January 1845 he suffered from hepatitis and died on 9 February.