Acts 12 reports that James the son of Zebedee was put to death by Herod Agrippa I:
1 Now about that time Herod the king stretched forth his hands to vex certain of the church.
2 And he killed James the brother of John with the sword.
This is generally held to indicate a death by beheading (though other forms of execution via a sword are possible).
Agrippa was a vassal of Rome, suggesting he may well have used Roman punishment (e.g. crucifixion), but he was also (at least in theory) a Jewish ruler, suggesting he may have used the Jewish method of execution (stoning).
Why would James have been executed by beheading? Wasn't this the more humane Roman method of execution reserved for Roman citizens? Was James a Roman citizen, or otherwise sufficiently prominent to treated with more respect than Jesus or Stephen?
Note that early Christian historians indicate that Peter was executed by crucifixion--but Paul, a Roman citizen, was executed by beheading.