Matthew Cole is James Cole's father.
Matthew was working in a car repair shop when Cassandra Railly and Katarina Jones came to see him to get a blood sample from the 2015 version of Cole. He initially gave them a pseudonym and told them that Matthew Cole was nowhere to be found, but Cassandra recognized the 2015 version of Cole playing outside. When Railly told him the story of the adult Cole being a time traveler, he tried to drive them off at gunpoint, but stopped after Railly mentioned the Army of the 12 Monkeys. He told Railly that Cole's mother, Marion, had left Cole with him, saying that she could not keep Cole safe from the Army. He went with Cassandra and Jones and met the adult Cole. The two had a brief but emotional reunion. Later, when the Army attacked Cassandra's bookstore, Matthew tried to protect the 2015 Cole, but was shot dead by the Pallid Man, while the 2015 Cole watched.