Transport and retention of multi-sized suspended granules are common phenomena in fracture media of oil, gas and geothermal reservoirs. It can lead to severe permeability damage and productivity decline, which has a significant impact on the efficient development of underground resources. However, the granule transport and retention behaviors remain not well understood and quantified. The novel stochastic model is proposed for the multi-sized suspended granule transport in naturally fractured reservoirs accounting for granule retention and fracture clogging kinetics. A percolation fracture network is proposed considering fracture connectivity evolution during suspended granule transport. Granule retention and fracture clogging dynamics equations are proposed to account for incomplete fracture clogging by retained granules. The microscale stochastic model is allowed for upscaling to predict the multi-sized granule transport behavior in naturally fractured reservoirs. The model solution exhibits preferential plugging of fractures with sizes equal to or below the granule size. Multi-sized suspended granule shows great advantages over mono-sized suspended granule in the control of permeability damage induced by granule retention and fracture clogging. The retained granule concentration and permeability damage rate decrease with fracture network connectivity improvement. The experimental investigation on size-exclusion suspended granule flow has been performed. The model-based prediction of the retained granule concentration and permeability variation history shows good agreement with the experimental data, which verifies the developed model.