The transport and deposition of particles over a fixed obstacle set in a fluid flow is investigated numerically. A two-dimensional model, based on lattice Boltzmann (LB) method and discrete element (DE) method, is used to simulate particle deposition. The corresponding method is two-way coupling in the sense that particle motion affects the fluid flow and reciprocally. The particle capture efficiency, as a function of particle size and Stokes number, is investigated using one-way (effect of the particle on the fluid is not considered) and two-way coupling respectively. The numerical simulations presented in this work are useful to understand the transport and deposition of particles and to predict the single fiber collection efficiency. The effect of obstruction shape on single fiber collection efficiency is investigated with LB-DE methods. Results show that the influence of particle on the flow field cannot be neglected for particles with large size. Numerical results for circular fiber collection efficiency are in good agreement with theoretical prediction and existing correlations. Enhanced collection efficiency is achieved by changing the fiber shape.