Electron transport in a linear atomic chain composed of 3 silicon atoms and sandwiched between gold electrodes is investigated with combination of density functional theory and non-equilibrium Green's function method. Relationship of conductance with distance is calculated. It shows that:At a distance of 1.584 nm, binding energy of junctions is minimum, structure is the most stable, Si-Si bond length is 0.216 nm, Si-Au bond length is 0.227 nm, conductance is 0.729 G₀(G₀=2e²/h), electron transport channels mainly consist of p_x, p_y orbital electrons of Si atoms. With increase of voltage conductance decreases and I-V curve of nanoscale junctions at equilibrium position shows linear feature.