An antenna structure is disclosed, which includes: a microwave substrate; and a first circuit, a second circuit, and a ground circuit disposed coplanarly on the microwave substrate. The first circuit is an open loop structure with a discontinuous portion and has a pair of ends, namely a feed point and a ground point, arranged respectively across the discontinuous portion. The ground point is connected to the ground circuit. The second circuit is disposed at the periphery of the first circuit, where the second circuit is connected to a connecting point of the first circuit on one side thereof. Thereby, the antenna structure reduces the SAR. In addition, an electronic device having an antenna structure is disclosed.