This paper considers the problem of linear parameter-varying (LPV) dual-rate system identification with slow-rate output data corrupted by random measurement delays. The local approach is used, and the LPV model is built through convex combination of several local linear models with time-varying weights. The dual-rate sampled data often exist in industry, and the measured output data are inevitably corrupted by random measurement delays. In order to handle random measurement delays and dual-rate sampled data in LPV system identification, the statistical description of the identification problem is established based on the presented output-interpolated LPV dual-rate model, and then, the proposed algorithm to estimate all the unknown model parameters, real output data, and measurement delays are derived in the generalized expectation–maximization algorithm scheme. One simulation example and a practical chemical process are used to verify the efficiency of the proposed method.