In this paper, a speaker adaptation method to adapt an existing speaking rate-dependent hierarchical prosodic model (SR-HPM) of an SR-controlled Mandarin TTS system to new speaker's data for realizing a new voice is proposed. Two main problems are addressed: data sparseness for few adaptation utterances existing only in a small range of normal speaking rate and no adaptation data in both ranges of fast and slow speaking rates. The proposed method follows the idea of SR-HPM training to firstly normalize the prosodic-acoustic features of the new speaker's speech data, to then train an HPM by the prosody labeling and modeling algorithm, and to lastly refine the HPM to an SR-dependent model. The MAP adaptation method with model parameter extrapolation is applied to cope with the above two problems. Experimental results on a male speaker's adaptation data confirmed that the resulting adaptive SR-HPM has reasonable parameters covering a wide range of speaking rates and hence can be used in the TTS system to generate prosodic-acoustic features for synthesizing the new speaker's voice of any given SR.