Citizens Advice Bureaux says the 51% increase means it is now Wales' biggest debt problem.
Council tax has increased by around 4% in the past year, and many cannot balance that with the cost of living.
The Welsh Local Government Association said it does its best to ensure the most vulnerable households are protected.
But the charity's report also found bailiffs knocked on the doors of 2,000 people last year in order to collect the tax.
A WLGA spokesman said: "In a period of such prolonged austerity, it comes as no surprise that the number of households reporting problems with paying their council tax has risen, on average bills are £160 less than in England.
"Council officers take an even-handed approach to enforcement."
Over 6,000 people are struggling to pay council tax bills in Wales - double the number a year ago, says an advice body.