Since stepping down as America's 43rd president in 2009, Bush has swapped his interest in political diplomacy for portrait painting, and this weekend he makes his debut as an amateur painter in an exhibition of more than 24 painted portraits of world leaders at the George W Bush Presidential Centre in Dallas.

Bush's first exhibition, The Art of Leadership, A President's Personal Diplomacy include portraits of Vladimir Putin, Tony Blair, Hamid Karzai, in traditional green cap and cape, and the Dalai Lama.

Bush has also captured the likenesses of the French president, Nicolas Sarkozy, the Canadian Prime Minister, Stephen Harper, Abu Dhabi's crown prince, Mohammed bin Zayed, and the former president of South Korea, Lee Myung-bak.

First impressions suggest Bush's portraits are not bad, says the Australian art critic John McDonald, who thinks Bush has the makings of a "good naive artist".

"They are deliberate, unsophisticated, and lacking any sense of his ability to model forms or volumes, but he manages to capture a likeness, and even something of the subject's personality. It's no worse than much of the work in the Archibald Prize!"

Bush's slightly lop-sided portrait of Putin is, says McDonald, probably the pick of the bunch.

But others have been less forgiving. The Telegraph's art critic, Alastair Sooke, described Bush's paintings as "dreary and compositionally identical likenesses" which "couldn't feel more impersonal if they tried".

"Nothing here has the surprising interest or sense of uneasy psychological penetration of Bush's bathroom self-portraits," says Sooke.

Like McDonald he found Bush's portrait of Putin to be the one exception. It was in summary "unconventional and compelling".

"It turns out that, whether artfully or not, Bush paints in a similar fashion to the way he talks – affecting a folksy, homespun, plain-speaking tone, with just enough ham-fisted strangeness and bungling missteps to keep things interesting."

Bush started his new hobby painting his pets, and then recently presented a portrait of Jay Leno to the Tonight show compere. He reputedly some days spends three or four hours at his easel.

The New York Times noted that Bush never had much time for museums and rushed through the Hermitage Museum in St. Petersburg, Russia, in 30 minutes flat. But he recently told a private gathering he could now linger in art exhibits for hours at a time studying brush strokes and colour palettes.

The Telegraph and The New York Times