The new branch has come up in Ang Mo Kio area, which is popular for its housing estates.
The SBI already operates branches in housing estates Marine Parade and the industrial estate of Jurong.
It has two branches in Little India precinct as well as one in the central business district.
"About 80 per cent of our customers are Chinese and the rest are high net worth Indians," said SBI country-head Soma Sankara Prasad after opening the Ang Mo Kio branch to a roaring lion dance, a Chinese tradition.
The new branch underlines the SBI's growing banking business in Singapore, he said.