Cust hit .240 with 25 homers and 70 RBIs last season but struck out 195 times, becoming the first player to lead in the AL in three straight seasons since Minnesota's Bobby Darwin from 1972-74. Cust whiffed 164 times in 2007 and 197 times in 2008.
He had 26 homers in 2007 and 33 the following year, and has topped Oakland for three consecutive seasons in homers, strikeouts and walks (93 last season).
Cust made $2.8 million last season and had been eligible for salary arbitration.
Oakland has three players remaining eligible for salary arbitration: right-hander Michael Wuertz and outfielders Rajai Davis and Scott Hairston.
General manager Billy Beane has been determined to add more power to the lineup. The A's last week acquired third baseman Jake Fox from the Chicago Cubs largely because they like Fox's bat.