The interval rough number rough sets model is the generalization of the classical rough sets. Since the lower approximation condition of interval rough number rough sets model is a full inclusion relation which is too strict to tolerate noisy data, strict conditions increase the possibility of a sample classified into a wrong class. To overcome the above shortcomings, an interval rough number variable precision rough sets model is proposed in this paper, which is combined with interval rough number similarity and the concept of variable precision rough sets. The model introduces the error parameter and can improve the tolerance of noise data. Then the related properties of the model are also proved. Moreover, we construct a maximal positive domain attribute reduction method based on the proposed model, which can process the data type of interval rough number without discretization. Finally, numerical examples are given to verify the rationality of the model.