His father held a small government post and he gave his children a careful education. He finished the school of the Kreuzkirche, Dresden. Then he completed his studies under Johann Christoph Schmidt (1664 - 1728), and profited much by the Italian operas which were performed at Dresden under the composer Lotti.
Graun's beautiful tenor voice secured him an appointment in the choir at Dresden. At an early age he composed a number of sacred cantatas and other pieces for the church service. After his voice had changed to a tenor, he made his debut at the opera of Brunswick, in a work by Schurmann, an inferior composer of the day; but not being satisfied with the arias assigned him he re-wrote them, so much to the satisfaction of the court that he was commissioned to write an opera for the next season. This work, Polydorus (1726), and five other operas written for Brunswick, spread his fame all over Germany. Other works, mostly of a sacred character, including two settings of the Passion, also belong to the Brunswick period. Frederick the Great, at that time crown prince of Prussia, heard the singer in Brunswick in 1735, and immediately engaged him for his private chapel at Rheinsberg. There Graun remained for five years, and wrote a number of cantatas, mostly to words written by Frederick himself in French, and translated into Italian by Boltarelli. On his accession to the throne in 1740, Frederick sent Graun to Italy to engage singers for a new opera to be established at Berlin. Graun remained a year on his travels, earning universal applause as a singer in the chief cities of Italy. After his return to Berlin he was appointed conductor of the royal orchestra (Kapellmeister) with a salary of 2000 thalers (£30). In this capacity he wrote twenty-eight operas, all to Italian words, of which the last, Merope (1756), is perhaps the most perfect. It is probable that Graun was subjected to considerable humiliation from the arbitrary caprices of his royal master, who was never tired of praising the operas of Hasse and abusing those of his Kapellmeister. In his oratorio The Death of Jesus Graun shows his skill as a contrapuntist, and his originality of melodious invention. In the Italian operas he imitates the florid style of his time, but even in these the recitatives occasionally show considerable dramatic power.