Australia's Ashleigh Barty made easy ork of her win against China's Saisai Zheng. Photo: Kirsty Wigglesworth/AP Photo

LONDON Ash Barty's express-train run to the top of the women's game shows no sign of slowing as the world number one dispatched China's Zheng Saisai 6-4 6-2 to reach the second round at Wimbledon on Tuesday.

Australian Barty, who followed up her French Open triumph last month by winning in Birmingham, sealed a 13th straight win in a brisk hour and 16 minutes, battling through the first set before easing through the second.

Barty has never been past the third round at Wimbledon, but her game is well-suited to the slick grass courts and, having dragged herself to the summit of women's tennis, she looks well-placed to challenge for a second Grand Slam title.

While some might feel the weight of expectation coming into a Grand Slam as world number one, it seems Barty is relishing the experience.

"It feels incredible. It feels a bit bizarre actually but I'm trying to go about my business in the same way as I always have done," she said.

"You have to enjoy every minute when you're playing at this beautiful tournament."

The 23-year-old will certainly have to overcome tougher challenges than the 43rd-ranked Zheng if she is to lift the trophy next Saturday.

They had played each other three times previously, with Barty winning on each occasion and, apart from a brief wobble in the first set when she allowed the Chinese to claw back from 3-0 down to 3-3, it was plain sailing.

She broke early in the second set and again in the eighth game to wrap up victory, volleying the winner before saluting the crowd.