Geometries of anionic, neutral and cationic small tungsten clusters Wn （n=3—6） are studied by the first principles method based on the density functional theory. For each of clusters studied, a number of low-lying states with specific geometries are found and some possible candidates for the global minimum are determined. It is found that all global minimum candidates have relatively low spins: singlet or triplet for the neutral clusters, and doublet or quartet for the ionic clusters. When n>3, the clusters undergo a transition from two-dimensional structure to three-dimensional structure, which is not the same as sliver clusters. In order to determine the most promising global minimum candidates for anionic clusters, the photoelectron spectra are simulated and the vertical detachment energy is calculated. All results obtained are in good agreement with available experimental data.