Hobart's Lord Mayor has declared he wants to "put the brakes" on Dark Mofo, saying the annual winter festival run by MONA is pushing the boundaries of good taste.

Ron Christie lashed out at what he described as the "shock festival" and suggested the Council may consider withdrawing its annual funding of $200,000 in cash and in-kind support.

Dark Mofo is now in its sixth year, and brings an estimated $50 million annually to the city.

Alderman Christie said he and his colleagues had been inundated with complaints about the festival, including the "unhealthy culture" it was generating.

"They say the mark of a good city is how well you look after your citizens, and I think the citizens have expressed their concerns about different aspects of Dark Mofo and which way it's going culturally," he said.

"Hobart is a community city, and it's Hobart, not Mobart."

The Lord Mayor says he was unimpressed with performance artist Mike Parr's street burial. ( Supplied: Dark Mofo/Remi Chauvin )

Alderman Christie said what began as a family event had been tarnished by controversies.

Last year animal liberation groups were outraged over a performance involving a bull carcass, and the appearance of giant inverted crosses around the city for this year's event has caused offence among Christians.

Alderman Christie was also less than impressed with performance artist Mike Parr's three-day burial beneath Macquarie Street.

"I'm not shocked anymore. It's not my cup of tea," he said.

Funding deal

The council's three-year funding deal for Dark Mofo is up for renegotiation this year, and Alderman Christie wants to sit down with the festival's creative director Leigh Carmichael to talk about its future.

"I think it's time now to put the brakes on. We're going too fast," he said.

Lord Mayor Ron Christie says Dark Mofo is "not his cup of tea". ( ABC News: Fiona Blackwood )

"I'm sure Mr Carmichael and [MONA founder David] Walsh would welcome conversations with any city that has a chequebook — maybe they should talk to Launceston."

Mr Carmichael said it was up to the council to decide which events it supports.

"We've had a longstanding relationship since Dark Mofo started in 2013 with the council, it's a relationship that we value," Mr Carmichael said.

"It's been very important to us and it's a significant sponsorship so we will just have to deal with that if it came to pass," he said.

He said there were no plans to move the festival, even if council support dried up.

"I think Dark Mofo belongs in Hobart, it's a Hobart-based event," he said.

"It would put pressure on us in certain areas, certainly in relation to the Winter Feast, but we'd look at it at the time."

Dark Mofo organisers say the inverted crosses are not there for shock value. ( Supplied: Mona/Dark Mofo/Rémi Chauvin )

Mr Carmichael was particularly disappointed with the community's reaction to the inverted crosses.

"There's a lot more going on with those than shock, that's not what we're doing it for," he said.

"We're raising issues around symbolism and religion and these are things that I want discussed and we want discussed as a festival."