This paper proposes a new kind of hidden Markov model (HMM) based on multi-space probability distribution, and derives a parameter estimation algorithm for the extended HMM. HMMs are widely used statistical models for characterizing sequences of speech spectra, and have been successfully applied to speech recognition systems. HMMs are categorized into discrete HMMs and continuous HMMs, which can model sequences of discrete symbols and continuous vectors, respectively. However, we cannot apply both the conventional discrete and continuous HMMs to observation sequences which consist of continuous values and discrete symbols: F0 pattern modeling of speech is a good illustration. The proposed HMM includes discrete HMM and continuous HMM as special cases, and furthermore, can model sequences which consist of observation vectors with variable dimensionality and discrete symbols.