The invention provides a well drilling method of a well containing hydrogen sulfide. The well drilling method of the well containing the hydrogen sulfide includes the following steps of confirming a first additive amount of a desulfurizer which needs to be added in drilling fluid according to the pre-added amount of the desulfurizer in the well containing the hydrogen sulfide and predicted hydrogen sulfide concentration of the well containing the hydrogen sulfide; performing first addition of the desulfurizer in the drilling fluid according to the first additive amount, obtaining first drilling fluid, and injecting the first drilling fluid into the well containing the hydrogen sulfide so as to perform drilling; and confirming second additive amount of the desulfurizer which needs to be added in the drilling fluid according to concentration of the desulfurizer in returned drilling fluid and the maintenance amount of the desulfurizer in the well containing the hydrogen sulfide, and performing second addition of the desulfurizer in the drilling fluid according to the second additive amount. The well drilling method of the well containing the hydrogen sulfide not only can improve the use effect of the desulfurizer in the well drilling process, but also avoids waste of the desulfurizer, and effectively reduces risks in drilling of the well containing the hydrogen sulfide.