Tungsten diboride, VVBv usually has a hexagonal structure with the space group P6(3)/mmc (number 194); and molybdenum diboride, MoB2, has a trigonal structure with R (3) over barm (number 166). Other than these phases, both diborides are reported to have a phase with an AlB2-type structure (P6/mmm, number 191). AlB2-type MoB2 is easy to synthesize and has been extensively studied, whereas AlB2-type WB2 is very difficult to synthesize and has appeared only once in a report by Woods et al. in 1966 (Woods, H. P.; Wawner, Jr., F. E.; Fox, B. G. Science 1966, 151, 75.) We have investigated these diborides by means of first-principles calculations and found that boron defects are responsible for the difference in their synthesizability. AlB2-type MoB2 became stable enough with some boron defects added, while AlB2-type WB2 became minimally stable, suggesting it may not actually exist. Following our calculations, we attempted to synthesize AlB2-type WB2 with the optimum quantity of boron defects but observed no trace of it. We conclude, from both calculations and experiments, that AlB2-type WB2 does not exist stably in the W-B phase diagram and that the compound produced in Woods et al.'s report might have contained some impurities.