The Reserve Bank of India has lowered its policy repo rate by 25 basis points to 7.5% after making a similar cut in mid-January.
The repo rate is the level at which the central bank lends to commercial banks.
Citing a weaker economy, both of the reserve bank's cuts this year have taken place outside scheduled policy meetings, surprising the market.
After the move, the rupee grew as much as 61.88 against the US dollar - its strongest since the beginning of February, while the benchmark BSE Sensex index rose 1.4% to hit a record high of 30,010.91 - the first time its crossed the 30,000 mark.
The action came after the authorities delivered its first annual budget last week and days after the central bank and government agreed to introduce inflation targets.
Central bank governor Raghuram Rajan said softer inflation and the government's commitment to fiscal discipline were factors behind the easing measure.
"Softer readings on inflation are expected to come in through the first half of 2015-16 before firming up to below 6% in the second half," he said in a statement on Wednesday.
Because of falling oil prices, India's inflation has eased sharply from last year and rose to an annual 5.11% in January - well below the reserve bank's 6% target.
