Serena Williams believes she still has plenty of room for improvement after easing through the US Open first round.

The 23-time grand slam champion showed good signs on her way to a 6-4 6-0 win over Magda Linette in New York on Monday.

Williams holds a 13-5 win-loss record on her return this year, including reaching the Wimbledon final.

But the 36-year-old feels she still has a way to go with her form, saying: "Right now I just feel like I'm on the road to getting better.

"I'm just going to be on that road until I get there."

Williams needed an hour and 10 minutes to get past Linette, growing into the first-round clash and finishing with 23 winners.

The American said she knew what to expect from Linette, having seen the Pole in action at coach Patrick Mouratoglou's academy.

"I thought it was a good match. It was a great first-round match. Magda, she's such a fighter. She's a very hard worker," Williams said.

"I've seen her at Patrick's academy a few times, so I kind of knew what to expect tonight. It was a little bit of a relief to know what to expect.

"I think overall I had a little shaky start, but I got into it."