There were 8,007 homelessness applications between October and December 2013, a tenth lower than the same quarter of 2012.
The number of families living in temporary accommodation has also dropped to its lowest level for five years.
Families in temporary accommodation decreased by 3% during the year from 10,252 to 9,963.
Of these, 2,456 were households with children in temporary accommodation, a fifth lower than one year earlier.
Housing Minister Margaret Burgess said: "The Scottish Government is committed to supporting people of all ages who are homeless or at risk of becoming homeless.
"We have worked hard with local authorities over the past few years to develop services in which staff assist households to consider options and address their individual needs in order to help prevent homelessness before it occurs.
"Alongside this we are increasing the supply of affordable housing to ensure settled accommodation is available to households as quickly as possible to reduce time spent in temporary accommodation. This is a vital part of our efforts to build a better and fairer Scotland.
"Today's figures, which show a drop of 20% in the number of households with children in temporary accommodation as well as a 10% decrease in homeless applications, demonstrate that this is working.
"However, while we welcome this continued improvement, we are concerned that Westminster's welfare changes may undermine this good work.
"This Government aims to deliver at least 30,000 affordable homes - including 20,000 for social rent, over the life of this Parliament. Over the four years to March 2016, we will be making over £1.3 billion available for affordable housing.
"We will continue to work with councils and their partners to prevent homelessness and improve outcomes for households that do become homeless."