Here we report a label-free colorimetric method for protein assay based on the intrinsic peroxidase-like catalytic activity of DNA-hemin-graphene (DNA-GH) composite. By using aptamers as protein recognition elements, protein-mediated aggregation of the DNA-GH composite leads to the decrease or increase of the colorimetric signal depending on the sandwich or competitive design strategy. Thrombin and PDGF-BB were chosen as model analytes and the detection limits (LOD) by this method were estimated to be 0.5 nM and 5 nM, respectively. Compared to traditional ELISA method for protein detection, this method possesses the advantages of high sensitivity, simplicity, and low cost. In addition, by designing different DNA-modified hemin-graphene (GH) constructs, using proteins as inputs, the "OR" and "INHIBIT" logic gates were built. This procedure does not require chemical modification on the aptamer probes or analytes and circumvents the limitation associated with the number of target binding sites. Given the attractive analytical characteristics and distinct advantages of DNA-GH composite, the universal approach can be widely applied for the detection of diverse proteins and for the design of versatile logic gates.