[1] Wennersten was born in Uddevalla on the west-coast of Sweden and played golf from age 10.

As an amateur, representing Lyckorna Golf Club in Ljungskile south of Uddevalla, she won the Swedish Junior Match-play Championship in 1977 and the Swedish Match-play Championship in 1981, successfully defending the title in 1982.

[2] In 1984, Wennersten enjoyed a spell on the LPGA Tour, with a best finish of T38 at the MasterCard International Pro-Am.

[2] The following year she became the second Swedish golfer to win on the Ladies European Tour, after Kärstin Ehrnlund, when she won the Mitsubishi Colt Cars Jersey Open.

[3] She finished third at the 1985 British Women's Open at Moor Park Golf Club, 4 strokes behind Betsy King, and ended the season ranked 10th on the LET Order of Merit.