Noise suppression in speech signal has received great attention in signal processing research community. However, existing methods of noise suppression such as the time-domain Kalman filter suffers from the psychoacoustic and physiological characteristic feature while the spectral subtraction technique performed in the modulation domain is associated with remnant noise in the enhanced speech signal. Therefore, in this paper, a Modulation-Domain coupled Kalman-Spectral Filtering (MD-KSF) in a single channel system is proposed to address the aforementioned shortcomings in the two existing techniques. The simulation of the proposed coupled MD-KSF was performed in MATLAB software environment. The evaluation of the proposed coupled MD-KSF technique in terms of Spectral waveform, Mean Square Error (MSE) and Log Spectral Distance (LSD) was performed. Furthermore, Perceptual Evaluation of Speech Quality (PESQ) and Short-Time Objective Intelligibility (STOI) tests were employed to validate the quality and intelligibility of the proposed coupled MD- KSF using the NOIZEUS corpus data set. The proposed technique shows significant noise suppression over the existing techniques.