Last month, the 19-year-old scored his first victory in Formula 3 at Spa, the home of the Belgian GP, which is synonymous with his father's career.
Michael made his debut there in 1991 for Jordan and earned his first win in F1 the following year driving for Benetton.
Now, Mick, has won his first F3 race at Spa and says he is focusing on having a strong finish to the season and making the step up to Formula Two.
He said: "The goal is to win in F1, that is the aim. My dad had a huge influence on my career.
"He was my idol and I am following everything he did and see if I can use it myself and I am really happy with that."
Schumacher admits that his famous surname has helped "open doors" but he wants to make his own name in racing, and not just be known as the son of a seven-time world champion.
He added: "You still have to show what you can do. That's my goal. I want to prove that I am a proper racing driver and not only show I have got the same name.
"F3 is an important step for that, and the next step has to be Formula 2, but my goal is to step up and show what I can do.
"It is a category you have to go through if you want to be a complete racing driver. I am happy I made the step to F3 and I feel ready to push through.
"We have a lot of people in F1 who went through F3 and it is a point where you can show what you've got."
Schumacher drives for the Prema Powerteam Dallara-Mercedes team while his father also drove for Ferrari.
However, Mick says that he has no preference as to whether it would be the German of the Italian team, so long as he makes it to F1.
He said: "I have no preference, both teams are amazing.
"I want to be a racing driver in F1 because that is where the best drivers are and I want to race against them and fight for it.
"The pressure is one everybody. We all want to be the best and want to win."
Hear the full interview with Mick Schumacher on BBC Radio 5 Live Formula One, Thursday 7.30pm or download The Chequered Flag podcast.
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