Born as a man, Ms Grodzka, now 57, completed her gender change last year with the help of the Trans-Fuzja organisation focused on gender change.
Topping the Palikot Movement party list in the devoutly Catholic southern city of Krakow - once home to the late Polish-born pope John Paul II - Ms Grodzka was thrilled by Sunday's strong showing at the polls.
"I'm not yet sure if I've been elected, but I'm very happy with the result scored by the Palikot movement," she said at a jubilant election night celebration at Palikot Movement headquarters in Warsaw.
"If I'll be elected in Krakow, I'll be Poland's first transgender woman, and the only transgender MP not only in Poland, but the entire world," she said. "In New Zealand, there was Georgina Beyer, but she is no longer an MP since 2007," Ms Grodzka added.
"Today, Poland is changing. I am the proof along with Robert Biedron, a homosexual and the head of an anti-homophobia campaign who ran for office in Gdynia," a city on Poland's Baltic coast.
Yep. We have a transgender woman and a big out there gay in the Parliament. In the addition to it, a few more unusual and quite out of the mainstream personas... Right in the faces of the tea party mentality PiS and other parties. Finally some anti-clerical, pro social change and openness politicians. We will see how well they do, but I am hopefull :)