Deep neural networks (DNNs) have been widely deployed across diverse domains such as computer vision and natural language processing. However, the impressive accomplishments of DNNs have been realized alongside extensive computational demands, thereby impeding their applicability on resource-constrained devices. To address this challenge, many researchers have been focusing on basic neuron structures, the fundamental building blocks of neural networks, to alleviate the computational and storage cost. In this work, an efficient quadratic neuron architecture distinguished by its enhanced utilization of second-order computational information is introduced. By virtue of their better expressivity, DNNs employing the proposed quadratic neurons can attain similar accuracy with fewer neurons and computational cost. Experimental results have demonstrated that the proposed quadratic neuron structure exhibits superior computational and storage efficiency across various tasks when compared with both linear and non-linear neurons in prior work.