In this paper, a structural maximum a posteriori (SMAP) speaker adaptation approach to adjusting the speaking rate (SR)-dependent hierarchical prosodic model (SR-HPM) of an existing SR-controlled Mandarin text-to-speech system to a new speaker's data for producing a new voice is discussed. Two main issues are addressed. One is the small SR coverage of the adaptation data and is solved by using the existing SR-HPM that was trained from a speech corpus of wide SR coverage as an informative prior. Another is the data sparseness problem resulting from the large number of parameters of the SR-HPM to be adjusted. It is solved by hierarchically organizing the SR-HPM parameters into decision trees so as to be efficiently adjusted by the SMAP method. The effectiveness of the proposed approach is evaluated on speech databases of five new speakers. Both objective and subjective evaluations show that the proposed method not only performs better than the maximum likelihood-based method in the observed SR range of the target speaker's data, but also is much better in the unseen SR ranges.