A new synthesis route for Pt nanoparticles by direct electrochemical reduction of a solid-state Pt ion precursor ($K_2PtCl_6$) is demonstrated. Solid $K_2PtCl_6$-supported polyethyleneimine (PEI) coatings on the surface of glassy carbon electrode were prepared by simple mixing of solid $K_2PtCl_6$ into a 1.0% PEI solution. The potential cycling or a constant potential in a PBS (pH 7.4) medium were applied to reduce the solid $K_2PtCl_6$ precursor. The reduction of Pt(IV) began at around -0.2 V and the reduction potential was ca. -0.4 V. A steady state current was achieved after 10 potential cycling scans, indicating that continuous formation of Pt nanoparticles by electrochemical reduction occurred for up to 10 cycles. After applying the reduction potential of -0.6 V for 300 s, Pt nanoparticles with diameters ranging from $0.02-0.5{mu}m$ were observed, with an even distribution over the entire glassy carbon electrode surface. Characteristics of the Pt nanoparticles, including their performance in electrochemical reduction of $H_2O_2$ are examined. A distinct reduction peak observed at about -0.20 V was due to the electrocatalytic reduction of $H_2O_2$ by Pt nanoparticles. From the calibration plot, the linear range for $H_2O_2$ detection was 0.1-2.0 mM and the detection limit for $H_2O_2$ was found to be 0.05 mM.