House prices in the UK rose by 7.5% in 2013, according to Halifax, but prices actually fell in December by 0.6%, the bank added.
Halifax said there are "mounting signs" that the economic recovery is becoming firmly established which, coupled with a decline in unemployment, will boost consumer confidence in the early part of 2014.
Martin Ellis, housing economist at Halifax, said: "This will increase the likelihood that more people will consider buying a property in 2014, therefore supporting housing demand.
"The recent strengthening in house prices is increasing the amount of equity that many homeowners have in their home. This will potentially encourage and enable more owners to put their property on the market for sale over the coming year, therefore boosting supply."
House prices in the final three months of 2013 were 1.9% higher than in the previous three months, the bank said. However, the December fall marked the first monthly decline since January 2013.
Busy start to 2014
Mark Harris, chief executive of mortgage broker SPF Private Clients, says: "2013 was a cracking 12 months for the housing market, which few had accurately forecast at the start of the year and 2014 has continued in the same vein. Mortgage brokers and estate agents have got off to an incredibly busy start as many buyers view this as the year when they will finally get on the housing ladder, or move up it.
"Rising property prices are fuelling fears among some buyers that if they don't act now, they will be priced out further, while falling unemployment has also raised concerns that interest rates will rise sooner rather than later."