At 76 years old, Kris Kristofferson is feeling his years. "I've begun soon to descend, like the sun into the sea," he admits on his new album, Feeling Mortal, a collection of immaculately observed originals with a similar autumnal glow to his friend Johnny Cash's American Recordings covers. Feeling Mortal finds Kristofferson embracing mortality with contentment, not regret, so it's a mystery why its songs don't feature in his live set.

Perhaps he's not feeling too mortal at the moment. In black shirt and jeans, the chiselled singer-actor-Rhodes-scholar looks fit and sturdy. However, the new, fragile tremor in his voice adds gravitas to a 90-minute journey through a remarkable life.

Performing mostly alone, with an acoustic guitar, harmonica and handkerchief – owing to the sniffles – he offers slow-paced songs rich in elemental imagery (daylight is "heavy with thunder"), set in lonely bars and roadside cafes. Taking in subjects from the plight of Native Americans to betrayal, drinking, redemption and the myth of freedom – with name checks for Barack Obama and Malcolm X – it's American history in song.

The wisdom and sincerity is humbling, but the septuagenarian retains his wit. Help Me Make It Through the Night turns into a joke about ageing. Some songs with his 22-year-old daughter Kelly allow him to quip: "She doesn't get her voice from me!" And when he sings about a night in the cells, he yells: "True story!"

Me and Bobby McGee – a posthumous hit for Janis Joplin – and hungover classic Sunday Morning Coming Down demonstrate the breadth of his impact. Lumps in throats meet his suggestion that "we may never pass this way again", but as the audience roar in protest he admits: "Aww, you make an old man very happy."

• What have you been to see lately? Tell us about it on Twitter using
#GdnGig