(S)-α-Ethyl-2-oxo-1-pyrrolidineacetamide (trade name levetiracetam), a derivative of piracetam, is used clinically as an add-on treatment for partial-onset seizures. In this study, we report the solid-state structure of a new drug co-crystal produced from levetiracetam and 3,5-dinitrosalicylic acid through cooling crystallization. This compound was further characterized by infrared spectroscopy, powder X-ray diffraction, and single-crystal X-ray diffraction. The new co-crystals show a 1:1 stoichiometry and crystallize in the monoclinic system, space group P21, with cell parameters: a = 9.7709(3) Å, b = 6.2202(2) Å, c = 14.7280(4) Å, α = 90°, β = 96.0340(10)°, γ = 90°, V = 890.16(5) Å3, and Z = 2. It is identified that hydrogen bonds are the main interactions between levetiracetam and 3,5-dinitrosalicylic acid, and the contribution of each hydrogen bond in maintaining the stability of the crystal structure was also quantified using Hirshfeld surface analysis.