The eight core sector industries -- coal, crude oil, natural gas, refinery products, fertiliser, steel, cement and electricity -- had expanded by 4 per cent in December 2013.
The growth was 6.7 per cent in November last year.
The core sector contributes 38 per cent to the overall industrial production, a parameter that RBI takes into account while framing its monetary policy.
Production of crude oil declined by 1.4 per cent, natural gas by 3.5 per cent, fertiliser by 1.6 per cent and of steel by 2.4 per cent in December 2014.
The growth in electricity generation declined to 3.7 per cent in December last year from 7.6 per cent in December 2013.
During April-December, the eight sectors grew by 4.4 per cent as against 4.1 per cent in the same period last year.