The 20-year-old Australian, who was seventh at the Olympic Winter Games this year, finished in 22nd place overall in Ruka.
Skiing in the dual moguls format, Graham comfortably defeated Ji-hyon Kim of Korea in the first elimination round with a score of 25-10.
In the next round, Graham faced American Thomas Rowley. In a close and exciting dual, both skiers were side-by-side coming into the bottom jump, but Graham unfortunately crashed out after losing a ski just before the final jump.
Graham is scheduled to next compete in Calgary, Canada, on January 4, which will be the World Cup round will be the first of three World Cups that Graham will use to prepare for the World Championships on January 18 in Kreischberg, Austria.
The Calgary World Cup is also expected to see the return of fellow OWIA/NSWIS athletes Britt Cox & Nicole Parks.
IMAGE: The course in Ruka, Finland © FIS