The Bank of England has an inflation target of 2%, but has failed to meet this for more than two years.
Analysts said the low rate of inflation meant it was unlikely the Bank would raise interest rates for some time.
The ONS said the main upward pressure on the inflation rate came from transport costs, which rose by 0.9% between April and May, partly due to higher diesel costs.
However, offsetting this was clothing and footwear prices, which dropped 0.2% between April and May, while food and drink prices fell 0.4%.
The rate of inflation as measured by the Retail Prices Index, which includes some housing costs, rose to 1.4% in May from 1.3% the month before.
In the years since the financial crisis of 2008, the Bank has been trying to lift economic activity and it has kept interest rates at record lows of 0.5% for seven years,
The Bank’s interest rate-setting committee, the Monetary Policy Committee, meets this week to discuss interest rates. At its last meeting, all nine members of the MPC voted not to change interest rates.
The Bank’s most recent forecast, in May, said inflation would remain below 1% until late into 2016, and would stay below the 2% target until 2018.