House price growth in the UK increased to 9.7% in the year to January, up from 9.5% a month earlier, according to the Halifax.
Britain's largest mortgage lender said the last time that figure was greater was in July 2014, when prices were rising by more than 10%.
Prices increased by 1.7% between December and January.
The Halifax said that the average cost of a house or flat in the UK had now risen to £212,430.
However, rival lender Nationwide has said the annual increase in the year to January was just 4.4%.
"The imbalance between supply and demand continues to exert significant upward pressure on house prices," said Martin Ellis, Halifax's housing economist.
"This situation looks set to persist over the coming months. Further ahead, increasing affordability issues, as price increases continue to exceed wage growth, are likely to curb housing demand and cause price growth to ease."