This paper proposes a recovery method of broadband speech form narrowband speech based on piecewise linear mapping. In this method, narrowband spectrum envelope of input speech is transformed to broadband spectrum envelope using linearly transformed matrices which are associated with several spectrum spaces. These matrices were estimated by speech training data, so as to minimize the mean square error between the transformed and the original spectra. This algorithm is compared the following other methods, (1)the codebook mapping, (2)the neural network. Through the evaluation by the spectral distance measure, it was found that the proposed method achieved a lower spectral distortion than the other methods. Perceptual experiments indicates a good performance for the reconstructed broadband speech.