Speech bandwidth expansion is used to enhance the auditory quality by artificially recovering the lost components in the high-band spectrum of narrow-band speech. Aiming at the problem of excitation expansion in speech source-filter extension model, a piecewise extension method was proposed. The higher spectrum part in the narrow-band excitation source and the white noise with the equivalent narrow-band excitation frame energy were used as the excitation sources for the lower and upper part of the extension band respectively. At last, the wideband excitation signal was composed of the above two and the original narrow band one. Experimental results of the wide band speech reconstruction with Hidden Markov Model (HMM) based spectrum envelope estimation show that the proposed method is superior to spectrum shift excitation expansion method.