The number of people approaching the charity for accommodation has almost doubled in the last few years - jumping from 1,972 in 2009/10 to 3,652 in 2010/11.
Meanwhile, 5,047 households presented as homeless to the Northern Ireland Housing Executive during April to June last year, an increase of 21% compared to the same quarter in 2011.
The Simon Community's new Freephone Helpline received 13,400 calls, the latest statistics revealed.
Carol O'Bryan, the organisation's chief executive, said that increasingly they're dealing with the 'new homeless.'
She described them as people who have been living fairly comfortably until hit by job loss, family break up or another crisis.
"Their savings soon run out and suddenly they find they can't meet the mortgage payments or pay the landlord.
"Often they turn in desperation to the quick fix loans they see advertised on TV, not realising that the high interest charged by many will only add to their problems."
Ms O' Bryan said that these families "don't fit society's traditional stereotype of the homeless."
She explained: "They aren't running away from anything; they are not transitioning out of care: they don't have mental health issues, alcohol or substance abuse problems."
"Their pride means that they often hide their difficulties and the family support system which - thankfully - still exists in Northern Ireland means that they are more likely to be 'sofa surfing' around relatives' homes than actually on the streets."
The charity has often stated that many people are just a few pay packets away from homelessness and are calling for active intervention immediately to stop it spiralling out of control.
The sweeping changes currently proposed through Welfare Reform will add to society's problems, Ms O'Bryan added.
"We are eager, together with others in the voluntary sector, to work with Government to create positive change, but the problems with Welfare Reform need to be addressed immediately or the risk of homelessness will increase."