This paper is concerned with parameter and output estimation for industrial processes described by finite impulse response model in presence of randomly missing output measurements. The statistical models for describing the estimation problems are given and the prior distributions over unknown parameters and variables are constructed. The estimation problems with incomplete dataset are formulated in the variational Bayesian framework and the problems of randomly missing measurements, overfitting, and high sensitivity of parameter estimate to noise are handled simultaneously. The iterative formulas to estimate the posterior distributions of missing output data and unknown parameters based on available process data are derived. The simulation example and the hybrid tank system experiment are performed to demonstrate the effectiveness of the proposed method.