Kojo polled 219 votes to beat his closest contender, John Obiri-Yeboah, who managed 145 votes.
The third contender, Bright Acquah managed a meager 40 votes out of a total 419 votes cast.
The Electoral Commission is yet to declare him winner as voting is officially expected to end at 3:00pm.
Oppong-Nkrumah voting earlier.
The incumbent MP, David Oppong Kusi, who has been in Parliament on three occasions, decided not to contest the seat again after 2016.
The seat, which appears to be a safe one for the NPP, is expected to be retained by Kojo Oppong-Nkrumah.
In the last election in 2012, the NPP stretched the margin by over 10,000 votes against the National Democratic Congress, NDC.
Voting commenced Saturday morning in some 244 constituencies across the country to elect new candidates who will wrestle power for the NPP in the 2016 parliamentary elections.
Some 30 constituencies are not taking part in the polls due to various internal wrangling some of which have become a subject of legal tussle.
But the number is now 31, following the suspension of polls in the Sawla-Kalba constituency of the Northern Region due to issues with ballot papers.
In most constituencies voting started at 8am with some starting a bit later. But for the incident in the Asokwa constituency where a former MP and an aspirant, Maxwell Kofi Jumah was arrested for vandalizing election materials, very few of such incidents have been reported in other parts of the country.
Voting is expected to end at 3:00pm, but counting has already started in most constituencies.
By: Ebenezer Afanyi Dadzie/3news.com/Ghana