In this paper, the Merged Delay Transformation approach has been employed in order to design Infinite Impulse Response-Decimation Filter (IIR-DF) and it has also been proved that this approach is an efficient approach for designing IIR-DF. In the proposed approach called as; MDT-IIR-DF, filtering followed by Sampling Rate Compression (decimation process) is obtained in a single stage instead of two separate stages as in conventional IIR Filters which in turn reduces the cost of computation in terms of number of multipliers per output samples. Two Examples have been included which show that the cost of computation for proposed approach; MDT-IIR-DF is low as compared to the cost of computation for various conventional Filters like: Polyphase FIR, Conventional IIR and Polyphase IIR, respectively. The proposed approach; MDT-IIR-DF is better computationally efficient in which the computational efficiency is increased by merging the M number of delay elements in recursive part together so that the current output can be directly computed from Mth old output. Magnitude and Phase Response of various MDT based IIR filters like; Butterworth, Chebyshev-I, Chebyshev-II and Elliptical flters have been compared with conventional Butterworth, Chebyshev-I, Chebyshev-II and Elliptical IIR filters (without MDT approach). The simulation results show that same magnitude and phase response for both (with and without MDT approach) filters i.e. the MDT based IIR-DF has close agreement with conventional IIR filter at low computational cost along with afficient architecture.