Inductive Output Tube (IOT) represents the latest generation of amplification technology employed in high-power applications. Owing to their electrical efficiency and established reliability, IOTs are gaining acknowledgment as RF sources within industrial, plasma heating, research and scientific domains. In an IOT, electron gun is not an independent component but is integrated with input cavity. This study focuses on the design of a planar cathode electron gun used in an IOT. The integration of electron gun with the input cavity within the IOT is highlighted, with its significance in efficient RF signal amplification. The design optimizes electrode geometry and dimensions using the Pierce Synthesis approach, with specific attention to grid dimensions and the cathode-grid gap to enhance density modulation and electron bunching. An electron gun for an IOT operating at a frequency of 350 MHz with a 4 A beam current is presented along with the fine-tuning of grid dimensions to facilitate effective modulation and the gap between the cathode and grid deliberately minimized to improve efficiency. The research provides valuable insights and ways for further advancements in increasing the applications of high-power IOTs.