A stochastic model of stroke order variation is proposed and applied to the stroke-order free on-line Kanji character recognition. The proposed model is a hidden Markov model (HMM) with a special topology to represent all stroke order variations. A sequence of state transitions from the initial state to the final state of the model represents one stroke order and provides a probability of the stroke order. The distribution of the stroke order probability can be trained automatically by using an EM algorithm from a training set of on-line character patterns. Experimental results on large-scale test patterns showed that the proposed model could represent actual stroke order variations appropriately and improve recognition accuracy by penalizing incorrect stroke orders.