A fastening structure of a clean container is combined on a cover of the clean container with a dismountable fastener member, such that the cover is closed or opened on a base of the clean container. The fastener member includes a body, a positioning portion, and an elastic fastening arm, that are one-piece formed. The positioning portion extends from one side of the body to form a flat spring. A flange is formed on the flat spring to fasten the fastener member on the cover. The elastic fastening arm has an elastic arm, and a lateral flange is formed on one end of the elastic arm, and extends into the base to be buckled. The fastener member further includes an elastic auxiliary arm formed between the elastic arm and the body, so as to increase an elastic strength of the elastic fastening arm.