Abstract This paper is concerned with the identification problems of linear parameter varying (LPV) systems with randomly missing output data. Since one local linearized model cannot capture the global dynamics of the nonlinear industrial process, the multiple-model LPV model in which the global model is constructed by smoothly weighted combination of multiple local models is considered here. The problem of missing output variables data is commonly encountered in practice. In order to handle the multiple-model identification problems of LPV systems with incomplete data, the local model is taken to have a finite impulse response (FIR) model structure and the generalized expectation-maximization (EM) algorithm is adopted to estimate the unknown parameters of the global LPV model. To avoid the problems of ill-conditioned matrices and high sensitivity of parameters to noise, the prior information on the coefficients of each local FIR model is employed to construct the prior probability of unknown parameters. Then the maximum a posteriori (MAP) estimates of the global model parameters are derived via the generalized EM algorithm. The numerical example is presented to demonstrate the effectiveness of the proposed method.