Different priesthoods in the Bible include the Levitical priesthood, Melchisedec, and priesthoods of idolatrous gods. Jesus Christ was a priest after the order of Melchisedec because the Levitical priesthood could not bring perfection. Jesus Christ was also from the tribe of Judah, not Levi, so he could not have been a Levitical priest. Christ was a priest after the order of Melchizadec.
Heb 7:1-3 ¶ For this Melchisedec, king of Salem, priest of the most high God, who met Abraham returning from the slaughter of the kings, and blessed him; 2 To whom also Abraham gave a tenth part of all; first being by interpretation King of righteousness, and after that also King of Salem, which is, King of peace; 3 Without father, without mother, without descent, having neither beginning of days, nor end of life; but made like unto the Son of God; abideth a priest continually.
Christ, having neither beginning of days, nor end of life, abides as a priest continually. This righteous priest, offered himself once for the sins of mankind, then sat down at the right hand of the Father.