In 1819, he was the library secretary of Uppsala University. The following year he was named as a lecturer in history at the university, and he later taught at the Military Academy Karlberg. In 1835 he was appointed as a pastor in Umeå, where he lived until his death.
He was admitted into the Swedish Academy in 1839, occupying Seat 6.
Grafström belonged to the literary circle centred on Malla Silfverstolpe. He wrote a famous biography of his father-in-law Frans Michael Franzén.
Some of Grafström"s poetry was set to music by the composer Johan Erik Nordblom. In his later years, Grafström was a vocal exponent of the expansion of the railway network into Norrland.
He died at Umeå, aged 80.