The 30-share barometer, which had gained 33.07 points in yesterday's trade, moved up further by 51.50 points, or 0.28 per cent, to 18,662.27.
Stocks of auto, consumer durables and banking sector led the rise.
Similarly, the wide-based National Stock Exchange index Nifty gained 14.35 points, or 0.25 per cent, to 5,674.60.
The trading sentiment remained firm on continued buying by funds and retail investors tracking overnight gains at the European and the US markets after an unexpectedly strong US housing data, brokers said.
In Asia, Hong Kong's Hang Seng rose by 0.52 per cent, while the Japan's Nikkei gained 1.66 per cent in early trade today.
The US Dow Jones Industrial Average ended 0.04 per cent higher in yesterday's trade.