Model-based image coding applied to interpersonal communication achieves very low bit-rate image transmission. To accomplish it, accurate three-dimensional (3-D) motion estimation of a speaker is necessary. A new method of 3-D motion estimation is presented, consisting of two steps. In the first, facial contours and feature points of a speaker are extracted using filtering and Snake algorithms. Five feature points on a speaker's facial image are tracked between consecutive picture frames, which gives 2-D motion vectors of the feature points. Then, in the second step, the 3-D motion of a speaker's head is estimated using a three-layered neural network model, after training with many possible motion patterns of the human head using an existing 3-D general shape model. Experimental results show that our method not only achieves good results but is also more robust than existing methods, even when the motion of an object is rather large or complicated. Accurately estimated 3-D motion parameters can realise image transmission at a very low bit rate.