This paper presents a new feature compensation approach to noisy speech recognition by using piecewise linear approximation (PLA) of an explicit model of environmental distortions. Two traditional approaches, namely vector Taylor series (VTS) and MAX approximations, are two special cases of our proposed approach. Formulations for maximum likelihood (ML) estimation of noise model parameters and minimum mean square error (MMSE) estimation of clean speech are derived. A hybrid approach of using different approximations for different types of noisy speech segments is also proposed. Experimental results on Aurora2 and Aurora3 databases demonstrate that the proposed approaches achieve consistently significant improvements in recognition accuracy compared to the traditional VTS-based feature compensation approach.