The ZnO thin films were grown on GaN template substrates by RF magnetron sputtering at different RF powers and n-ZnO/p-GaN heterojunction LEDs were fabricated to investigate the effect of the RF power on the characteristics of the n-ZnO/p-GaN LEDs. For the growth of the ZnO thin films, the substrate temperature was kept constant at $200^{circ}C$ and the RF power was varied within the range of 200 to 500W at different growth times to deposit films of 100 nm thick. The electrical, optical and structural properties of ZnO thin films were investigated by ellipsometry, X-ray diffraction (XRD), atomic force microscopy (AFM), photoluminescence (PL) and by assessing the Hall effect. The characteristics of the n-ZnO/p-GaN LEDs were evaluated by current-voltage (I-V) and electroluminescence (EL) measurements. ZnO thin films were grown with a preferred c-axis orientation along the (0002) plane. The XRD peaks shifted to low angles and the surface roughness became non-uniform with an increase in the RF power. Also, the PL emission peak was red-shifted. The carrier density and the mobility decreased with the RF power. For the n-ZnO/p-GaN LED, the forward current at 20 V decreased and the threshold voltage increased with the RF power. The EL emission peak was observed at approximately 435 nm and the luminescence intensity decreased. Consequently, the crystallinity of the ZnO thin films grown with RF sputtering powers were improved. However, excess Zn affected the structural, electrical and optical properties of the ZnO thin films when the optimal RF power was exceeded. This excess RF power will degrade the characteristics of light emitting devices.