This paper presents a speech enhancement approach derived by using a piecewise linear approximation (PLA) of an explicit model of environmental distortions. PLA is a generalization of two traditional approaches, namely vector Taylor series (VTS) and MAX approximations. Formulations are described for both maximum likelihood (ML) estimation of noise model parameters and minimum mean-squared error (MMSE) estimation of clean speech. Evaluation experiments are conducted to enhance speech signals corrupted by several types of additive noises. Compared to the traditional MAX-approximation based approach, our PLA-based speech enhancement approach achieves better performance in terms of two objective quality measures, namely segmental SNR and log-spectral distortion.