Annie Holmström played at the 1912 Stockholm Olympics, both in the outdoor and covered court (indoors) competition. She made the quarter-finals in singles both in- and outdoors. In mixed doubles she and Torsten Grönfors made the semi-finals but lost, and then lost the bronze medal match to place fourth. Holmström was a losing finalist at the 1911 and 1913 Swedish Covered Courts Championships. She started playing tennis with her sister, Ellen Brusewitz, with Jönköping Lawn Tennis Klubben, but later moved to KLTK (Kungliga Lawn Tennis Klubben).