The grain growth in the polycrystalline ceramic fibers at elevated temperatures is controlled by the porosity that can lead to the abnormal behaviour. To investigate this process in detail we propose a combined model which couples the multiphase-field approach to the pore evolution equation. Two variants of the interaction function of pores and grain boundaries are suggested: with and without additional phase-field order parameters responsible for the pores. It is shown that both variants can reproduce the contact angles in triple junctions by choosing appropriate model parameters. For each variant, the dependency of the grain boundary drag velocity on the pore diffusion coefficient are studied numerically. The grain size evolution for different values of pore diffusion coefficients, pore fraction and initial pore size are investigated and the precision of the both model variants is discussed. The comparison with previous theoretical results and the experimental observations shows a good agreement.