A cover assembly and a battery are disclosed. The cover assembly is configured to cover a housing provided with an accommodating cavity in the battery and includes a top cover and an anode piece. The top cover is configured to be connected to the housing and cover the accommodating cavity, the top cover has a top surface away from the accommodating cavity, and the top surface is recessed towards the accommodating cavity to form a counterbore. The anode piece is disposed on the top cover, the counterbore is configured to accommodate the anode piece, the anode piece has an upper surface away from the accommodating cavity, and the upper surface is coplanar with the top surface; or the upper surface is closer to the accommodating cavity with respect to the top surface.