The present disclosure provides a secondary battery and a battery module. The secondary battery includes an electrode assembly, a case and a cap assembly. The case has an accommodating cavity, and the electrode assembly is accommodated in the accommodating cavity. The electrode assembly comprises electrode units stacked in an axial direction of the accommodating cavity. The cap assembly comprises a cap plate and a vent piece, the cap plate is connected with the case and positioned at a side of the electrode assembly in the axial direction. The cap plate is provided with a through-hole, and the vent piece covers the through-hole. The cap plate has a first inner surface, the vent piece has a second inner surface, and a distance between the first inner surface and the electrode assembly is larger than a distance between the second inner surface and the electrode assembly.