Grossi started playing tennis at the age of eight. On the WTA Tour , she won an individual title at the San Marino Open in 1993 . In the final, she defeated Barbara Rittner 3: 6, 7: 5 and 6: 1. Her best Grand Slam result in singles was the third round of the 1994 French Open .
For the Italian Fed Cup team , she played two games in doubles in 1994, none of which she won.