Francesca Jones, 15, was born with Ectrodactyly Ectodermal Dysplasia and faces issues with balance, and gripping her racquet.
Jones lost in round two of Wimbledon's junior tournament this week.
"I know I have the level of a top-five player so I'm just going to go for it," she said.
Ectrodactyly Ectodermal Dysplasia is caused by a mutated gene, and Jones has had three operations this year alone.
"If I have to do the operations again, I'll do them again," she said. "Everything's mental and everything's work, so if you keep at it then eventually it's going to work out for you."
When Jones started playing tennis, she needed special handles fitted to her racquet.
At the age of nine she decided to move to a tennis academy in Barcelona and was number four in the world at under-14 level.
"I got to the point where I thought with my condition, I could have a massive point that I could prove here to people, that willpower and determination is everything in life," she added.
"I have three toes on my right foot which is obviously my dominant foot, so balance had always been a weakness of mine.
"As I matured, as I got older, I have just worked on that day in, day out."
After a "disappointing" 4-6 7-5 6-1 defeat by fifth seed Kayla Jones in the singles, Jones is competing in the Wimbledon girls' doubles with Ali Collins.
A British teenager with a rare condition that left her without two fingers and three toes says it will not stop her becoming a top tennis player.