A novel polyacrylonitrile (PAN) nanofibrous membrane conjugated with platinum nanoparticles (PtNPs) was fabricated by electrospinning and electrostatic assembly techniques. In this procedure, PAN was electrospun with 3-aminopropyltriethoxysilane (APS) together as precursor materials. First, amine groups were introduced onto PAN nanofibers, and then the as-prepared negative-charged platinum nanoparticles (PtNPs) were conjugated onto the surface of the amino-modified PAN nanofibers uniformly by the electrostatic interaction-mediated assembly. The fabricated PAN-PtNPs hybrid nanofibrous membrane was further utilized to modify the glassy carbon electrodes and was used for the fabrication of a non-enzymatic amperometric sensor to detect hydrogen peroxide (H2O2). The electrochemical results indicated that, due to the uniform dispersion of PtNPs and the electrostatic interaction between amine groups and PtNPs, the fabricated PAN-PtNPs nanofibrous membrane-based electrochemical sensor showed excellent electrocatalytic activity toward H2O2, and the chronoamperometry measurements illustrated that the fabricated sensor had a high sensitivity for detecting H2O2. It is anticipated that the strategies used in this work will not only guide the design and fabrication of functional polymeric nanofiber-based biomaterials and nanodevices, but also extend their potential applications in energy storage, cytology, and tissue engineering.