Klaasen beat Kevin Burness 3–1 in the first round of the 2020 PDC World Darts Championship, before losing to Michael van Gerwen by the same scoreline. At the 2020 UK Open, he started his campaign by defeating Riley's qualifier Jason Askew 6–4. Klaasen then beat William Borland 10–5 before thrashing Steve West 10–1 to set up a sixth-round clash with Gary Anderson. He overcame Anderson 10–9 before losing in the quarter-finals to Daryl Gurney.