Forex traders said positive domestic equities and weak US currency supported the local unit. Moreover, investor sentiment strengthened after Pfizer reported encouraging vaccine test results.
The rupee opened at 75.51 against the US dollar, gained further ground and finally closed for the day at 75.04 against the US dollar, up 56 paise over its previous close.
It had settled at 75.60 against the greenback on Wednesday.
In highly volatile trade, the domestic unit witnessed an intra-day high of 74.99 and a low of 75.53.
The first of four experimental COVID-19 vaccines being tested by Pfizer and its German partner BioNTech showed encouraging results in very early testing of 45 people, the companies said on Wednesday.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.26 per cent to 96.94.
The 30-share BSE benchmark Sensex was trading 550.35 points higher at 35,964.80 and broader NSE Nifty rose 154.40 points to 10,584.45.
Foreign institutional investors were net sellers in the capital market as they sold shares worth Rs 1,696.45 crore on Wednesday, according to provisional exchange data.
Brent crude futures, the global oil benchmark, rose 1.40 per cent to USD 42.62 per barrel.
Meanwhile, the number of cases around the world linked to COVID-19 has crossed 1.06 crore and the death toll has topped 5.16 lakh.
In India, the death toll due the disease rose to 17,834 and the number of infections spiked to 6,04,641, according to the health ministry. DRR ANS ANS