According to Exodus 34, a veil covered Moses' face after he spoke with God.
Exodus says Moses's face shone when he came down from Mount Sinai carrying the renewed covenant tablets. Aaron and the Israelites were afraid to approach him, so Moses spoke with them first. Afterward, he placed a veil over his face.
The passage distinguishes between Moses speaking to the people and Moses entering the presence of God. He removed the veil when he went in to speak with God and put it back afterward. This detail occurs near the end of the golden calf and covenant-renewal narrative.
The veil is sometimes confused with the curtain inside the Tabernacle. They are different objects: Moses's veil covered his face, while the Tabernacle's curtains and screen formed parts of the sanctuary. Exodus 34 does not describe Moses wearing a crown or mask.