Flow through and around fishing net cages is an important issue in aquaculture. A three-dimensional multi-relaxation time (MRT) lattice Boltzmann model was used to simulate the flow field around a plane net in a constant current. The model was validated with experimental data. The results show that this numerical model is applicable to and reliable for the investigation of the flow field around a fishing net and can provide the detailed velocity distribution in the net aperture. Based on this model, a series of simulations were carried out to analyze the influences of the net solidity and the current velocity on hydrodynamic characteristics and flow-velocity attenuation. The results indicate that the flow-velocity attenuation is mainly related to the net solidity of the plane net, with a higher velocity drop response related to a higher net solidity. These results provide fundamental information for further studies on the flow field around the fishing net cage, which has potential application in analyzing the impacts of biofouling on fishing nets.