In this paper, a Blind Speech Separation (BSS) technique is introduced based on Independent Component Analysis (ICA) for underdetermined single microphone case. In general, ICA uses noisy speech from at least two microphones to separate speech and noise. But ICA fails to separate when only one stream of noisy speech is available. We use Log Spectral Magnitude Estimator based on Minimum Mean Square Error (LogMMSE) as a non-linear estimation technique to estimate the speech spectrum, which is used as the other input to ICA, with the noisy speech. The proposed method was tested for machinery, babble and traffic noise types mixed with speech at Signal to Noise Ratios (SNRs) of -5 dB, 0 dB and 5 dB. Objective and subjective results show high quality and intelligibility in the separated speech using the developed method.