In offside detection during a football match, afterimage and occlusion confuse the linesman and the referee, and this confusion can cause judgment errors. This paper proposes a method of football-offside detection using multiple cameras in an automatic linesman assistance system. In this method, multiple cameras and offside detection units are installed as a hardware system, and offside will be alerted when at least one of the offside detection units detects offside. In an offside detection unit, when the offside position is determined, offside is immediately judged in the case in which the ball is passed from an attacker to another attacker who is located nearer the opponent-goal line than the most-back defender and the ball. The vertical lines that represent these attackers, defenders and ball are used as their positions for logically judging the offside. Experiments were performed using video clips from 381 tournaments of English Premier Leagues from 2016 to 2017. The results showed 98.50% accuracy compared with the expert.