Housing charity Focus Ireland experienced a 44% increase in the numbers using its services between 2012 and last year.
Its president, Sr Stanislaus Kennedy, has accused the Government of directly forcing people into homelessness.
She urged the Government to increase rent supplement immediately to prevent many families losing their homes.
Launching the charity's annual report today, Sr Stan said in 2012 it helped 8,000 people who were homeless or at risk of losing their homes and that figure rose to 11,500 last year.
The charity believes it is likely to help significantly more people by the end of this year.
Sr Stan said homelessness has now become a national emergency and the Government must accept that some of its policy decisions are directly responsible for this.
She recalled that, three years ago, the charity warned that many families were at a tipping point between home-occupancy and homelessness because rent supplement payments were not matching rising rent levels.
Back then, she recalled, eight families a month were becoming homeless in Dublin, but the Government did not heed the warnings.
Since then, there had been what she called "a staggering rise in family homelessness".
This year an average of 70 families are becoming homeless every month in the capital - with a record 83 families becoming homeless last month - while the problem is also growing around the country.
She said the Government could, with the stroke of a pen, increase rent supplement immediately to prevent many families losing their homes this month.
Focus Ireland also wants ministers to deliver on their promise of rent certainty and to introduce tax change.
Speaking on RTÉ’s News at One, Sister Stan said as well as an increase in rent supplement, the Government must freeze rents, introduce rent certainty, and ensure that there is a taxation system that will encourage landlords to rent their property.
She said if action is not taken now the situation will get worse with more and more families will find themselves homeless.
