Who was the only Roman emperor whose father, grandfather and great-grandfather were also rulers of the Empire?

Commodus, who reigned from 180 to 192 AD, was the only Roman emperor whose father (Marcus Aurelius), grandfather (Antoninus Pius), and great-grandfather (Hadrian) had all been emperors before him.

https://en.wikipedia.org/wiki/Commodus

Sounds plausible, but Antoninus Pius and Hadrian were not the biological grandfather and great-grandfather of Commodus; the succession was by adoption.
The emperor in question ruled in the 5th century.

There is the Heraclian branch of the Byzantine Emperors... How about, Tiberius IV ?

Tiberius IV reigned 706-711, who was the Son of

Justinian II reigned 685-695, 705-711, who was the Son of

Constantine IV reigned 668-685, who was the Son of

Constans II reigned 641-668, who was the son of

Constantine III reigned 641, who was the son of

Heraclius reigned 610-641

https://en.wikipedia.org/wiki/Family_tree_of_Byzantine_emperors

OK, then I change my answer to Valentinian III who reigned from 425-455 AD.

His father Constantius III ruled briefly as co-emperor, while his grandfather Theodosius I was one of the most important emperors in Roman history. Theodosius was the last emperor to rule over both the eastern and western halves of the empire. Valentinian's great-grandfather was Valentinian I, who founded the Valentinian dynasty.

https://en.wikipedia.org/wiki/Valentinian_III