Nope.. A person who once disbelieved can later come to believe and be saved.. So unbelief is a pardonable sin..
The only unpardonable sin is called Blasphemy of the Holy Spirit.. Jesus identified it when a scribe from Jerusalem committed it by declaring the Signs that Jesus did ( like healings and others) where done by the power of beelzebub the king of the demons..
Now Jesus did His miracles by the power of the Holy Spirit.. So the scribe was declaring that the Holy Spirit was a demon and thus he had blasphemed the Holy Spirit..
Mark 3: KJV
22 "¶ And the scribes which came down from Jerusalem said, He hath Beelzebub, and by the prince of the devils casteth he out devils. {23} And he called them unto him, and said unto them in parables, How can Satan cast out Satan? {24} And if a kingdom be divided against itself, that kingdom cannot stand. {25} And if a house be divided against itself, that house cannot stand. {26} And if Satan rise up against himself, and be divided, he cannot stand, but hath an end. {27} No man can enter into a strong man’s house, and spoil his goods, except he will first bind the strong man; and then he will spoil his house. {28} Verily I say unto you, All sins shall be forgiven unto the sons of men, and blasphemies wherewith soever they shall blaspheme: {29} But he that shall blaspheme against the Holy Ghost hath never forgiveness, but is in danger of eternal damnation: {30} Because they said, He hath an unclean spirit."