Linda McCrary-Fisher's performance of "Until Then" included the poignant lyric, "my heart will go on singing ... until the day God calls me home."
The congregation includes President Donald Trump, Vice President Mike Pence and their wives. The service is being streamed live online.
Neither Pence nor Trump spoke during the service, but they met privately with the family beforehand.
The Rev. Franklin Graham, who now is CEO of the Billy Graham Evangelistic Association, delivered the main funeral address for his father, urging mourners to accept salvation, after shorter messages from Billy Graham's three daughters and younger son.
He said, "the Billy Graham that the world saw on television, the Billy Graham that the world saw in the big stadium was the same Billy Graham that we saw at home. There weren't two Billy Grahams."
The funeral planning began a decade ago with Billy Graham himself, and reflected his family's desire to capture the feeling of the crusades that made him the world's best-known Protestant preacher of his era.
Graham, who died last week at age 99, brought a message of salvation to millions during visits and live broadcasts to scores of countries.
Graham will be buried next to his wife in a memorial prayer garden at the library, with his grandchildren serving as pallbearers.
Billy Graham - Through The Years