Figures obtained by the BBC show the number of families in temporary accommodation for six weeks also trebled over the same period in Medway, breaching government guidelines.
The Conservative-led authority said it may take up to four years before the situation improves.
The Labour opposition said the answer was to build more council homes.
Councillor Howard Doe, cabinet member for housing, said: "There are a range of social issues and we cannot afford to deal with them all now.
"I'm hoping that over the next three to four years I would expect the figures to improve.
"As universal credit comes in and any bumps are ironed out, I think landlords will be far happier taking people who are drawing benefits."
Council figures show the number of families in temporary accommodation rose from 85 in March to 148 by the end of 2014.
In the same nine-month period, the number of children in temporary accommodation rose from 145 to 305.
The number of families living in similar circumstances for six weeks or more trebled from 40 to 120, in the same period.
Government guidelines say B&B accommodation should only be used for families for a maximum of six weeks.
Councillor Teresa Murray, deputy leader of the Labour group, said there was a shortage of housing, with 20,000 people on the waiting list.
She said: "In my ward, I've got families living in two-bedroom flats and they have four children."
She said the answer was to build more council houses.
"Any temporary accommodation is dealing with the consequence and not the cause," Ms Murray added.
Numbers of children in temporary housing more than doubled between March and December, Medway Council says.