In this work, a graphene film was electrochemically functionalized by anodic oxidation of amine terminated PAMAM (4th generation PAMAM-(NH2)64) dendrimer molecules via covalent linkage (C-N) between graphene and PAMAM. In this, the simple functionalization provides ≈37.51×10 15 PAMAM molecules cm -2 on the versatile graphene, which is ten times higher than the PAMAM molecules attached on GCE (3.33×10 15 molecules cm -2 ). Thus, the facile electrochemical functionalization route on graphene yields a high density of amine functional groups on graphene which offers an opportunity to load more number of enzymes, proteins, DNA, antibodies, antigens, etc. to develop highly sensitive graphene based bio and chemical sensors. To demonstrate this with a model, horseradish peroxidase (HRP) enzyme was chosen and immobilized onto the functionalized graphene film to detect H2O2. The so constructed platform shows enhanced electrocatalytic activity, high storage stability up to one month, lower applied potential and exhibits a high sensitivity of 29.86 µA mM -1 cm 2 which was 5 times greater than the functionalized GCE for the detection of H2O2. The sensor was also used to detect H2O2 in human serum to testify the feasibility of the sensor in practical application. These results demonstrate that the electrografting of PAMAM on graphene is a promising approach for the fabrication of the sensors which exhibit enhanced electrocatalytic activity, sensitivity and stability.