In this paper, we study the application of two forms of edit distance (ED) in an on-line handwritten character recognition system which is based on vector quantization techniques (VQ). A learning ED and an adaptive ED are proposed respectively for tasks of codebook generation and character recognition. Here, the cost functions are constructed on the modelling precision of handwriting primitives. For the learning ED, the cost function is static and derived by evaluating the primitives globally on the whole training database. For the adaptive ED, the cost function becomes dynamic and is adapted to the modelling errors at each time instant. The built system is tested on an online handwritten character recognition application on the UNIPEN data corpus.