Staff at William Booth House said it was full most nights after demand for the hostel's services increased.
Principal project worker Graham Di Duca said the 113-bed building had "been on virtually 100% occupancy" for the past six months.
Local charities hope a new Â£5m hostel, opening next month, will help to address the problem of homelessness.
Mr Di Duca said the number of people seeking the Salvation Army's help had escalated in the past few months due cuts in support services.
He said: "It isn't a change in the causes of homelessness. It is certainly a change provision for the homeless that's creating this pressure.
"Budget cuts have undoubtedly had an impact on most service providers."
A new Â£5m hostel, named The Crossing, is set to open in August. Funded by Hull City Council and local charities, it will provide temporary accommodation for 46 people.
It replaces an older facility and will increase the total number of hostel beds available to the homeless in Hull by five.
One resident at William Booth House is Fred Clarke who became homeless after his relationship with his girlfriend broke down.
He has been homeless for a month and had to spend several nights on the streets before he managed to get a bed at the hostel.
Mr Clarke, who is visually impaired, said he thought he could not have survived more than a few days living on the streets.
He said: "It does get a bit scary at night-time and especially at weekends when everyone's been out drinking and they're getting a bit rowdy and that, and the police are flying around and ambulances.
"It does worry you a bit you are going to get picked on because you're laid there on a seat trying to get some sleep."
Hull's Salvation Army hostel says it is struggling to cope with the growing number of people needing its help.