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A linear model tree is a decision tree with a linear functional model in each leaf. Previous model tree induction algorithms have operated on the entire training set, however there are many situations when an incremental learner is advantageous. In this paper we demonstrate that model trees can be induced incrementally using an algorithm that scales linearly with the number of examples. An incremental node splitting rule is presented, together with incremental methods for stopping the growth of the tree and pruning. Empirical testing in three domains, where the emphasis is on learning a dynamic model of the environment, shows that the algorithm can learn a more accurate approximation from fewer examples than other incremental methods. In addition the induced models are smaller, and the learner requires less prior knowledge about the domain.