The speech enhancement problem covers a broad spectrum of constraints, applications and issues. The principal application areas of speech enhancement are noise reduction for human listening, preprocessing for recognition systems and preprocessing for linear predictive coding. This paper introduces a modified technique based on Multi-band envelope expansion technique called adaptive multi-band logarithmic envelope expansion technique. In this technique a threshold level varying according to the change of input signal-to-noise ratio is used, and the nonlinear function used to expand the envelope is a logarithmic function. In addition, the use of non-uniform frequency spacing gives better enhancement since the majority of filters are concentrated in the actual speech band ( up to 1.5 KHz ) with few filters in the remaining band 1.5 up to 4 KHz ). The simulation results show that the new technique gives a high dynamic range of input signal-to-noise ratio ( up to - 8db ), and a high improvement factor. The intelligibility of the proposed technique is considered as a subject for further investigation.