For better power utilization,area,speed which are important criteria in the design of DSP processors multiplier design is main issue.The work of multiplier is rounding the numbers both signed and unsigned.In few applications speed is more important than accuracy so to improve the performance approximate circuits are introduced with reduce energy consumption and increase speed.In this paper,we propose an FIR filter based on Modern Rounding Based Approximate(M ROBA).In this modified rounding based approximate multiplier the numbers are rounded to the nearest exponent irrespective of 2n .The proposed MROBA multiplier based FIR filter was compared with Rounding Based Approximate (ROBA) Multiplier. In this multiplier the operands are rounded to the nearest exponent of two. This approximation will lead to simplification of multiplication operation thus reducing area and increasing speed. MROBA gives better results with the MROBA MAC unit is implemented.