The firm, which runs over 60 stores across the UK and Ireland, said like-for-like sales lifted 5.3% over the six weeks to January 2, compared to a year ago.
The retailer - which sells such brands as Biba, Jacques Vert and Ted Baker - said online sales on Black Friday jumped 40% compared to 12 months ago and constituted its biggest ever online trading day.
The firm added it continued the good momentum throughout the period, with like-for-like sales in the seven days after Christmas lifting by 6.8% year-on-year.
By contrast, high street bellwethers Next and Marks & Spencer last week posted dips in trading over Christmas, as they coped with the warmest December in over 100 years.
House of Fraser chief executive Nigel Oddy said: "This year, we saw a very strong start to the key Christmas season with Black Friday being particularly strong online, with sales up 40% on the year - our biggest online day ever.
"Our stores have also performed well over the festive period, in particular our recently refurbished stores which showed strong growth in the final week before Christmas."
Rival department chain Debenhams will post its Christmas trading update on Tuesday as it battles to turn its business around.
Retail veteran former Kingfisher chief executive Sir Ian Cheshire is in discussions with Debenhams about taking over from current chairman Nigel Northridge after disappointing results in recent years, according to reports earlier this month.
Chinese conglomerate Sanpower Group bought a majority stake in House of Fraser, which was founded in 1849, for £480 million in 2014.