To say that John Wesley did not believe in predestination is not exactly accurate. The fact that Wesley did not believe in what is understood as a Reformed (Calvinistic) view of predestination or decrees is not to say that he did not believe in predestination.
Wesley, as an orthodox Christian, believed and taught that God in fact did predestine and decree the matters of salvation. He believed that God decreed and predestined that all who would believe will be saved and all who disbelieve will be lost (Sermon #58--On Predestination: see Resource tab and Wesley's sermons).
The difference here is that God has predestined and decreed the means of salvation and NOT the members of salvation. This is a critical difference that allows Wesley to affirm God as in charge of the matters of salvation as far as it relates to the means or way of salvation.
This distinction in predestination is critical. Wesley believed that the Reformed position of predestination and decrees that "selected" certain people (members) for salvation and certain people for damnation did too much damage to the character of God as seen in Jesus Christ. Where Wesley contends that God determines the way (means) of salvation.
REFLECT: How do each of these views affect your view of the character of God?