This paper presents the first phase of design,analysis,and simulation for the klystron coaxial radio frequency (RF) output window.This study is motivated by 800 kW continuous wave (CW),650 MHz klystrons for the future plan of circular electron-positron collider (CEPC) project.The RF window which is used in the klystron output section has a function to separate the klystron from the inner vacuum side to the outside,and high RF power propagates through the window with small power dissipation.Therefore,the window is a key component for the high power klystron.However,it is vulnerable to the high thermal stress and multipacting,so this paper presents the window design and analysis for these problems.The microwave design has been performed by using the computer simulation technology (CST) microwave studio and the retu loss of the window has been established to be less than-90 dB.The multipacting simulation of the window has been carried out using MultiPac and CST particles studio.Through the multipacting analysis,it is shown that with thin coating of TiN,the multipacting effect has been suppressed effectively on the ceramic surface.The thermal analysis is carried out using ANSYS code and the temperature of alumina ceramic is lower than 310 K with water cooling.The design result successfully meets the requirement of the CEPC 650 MHz klystron.The manufacturing and high power test plan are also described in this paper.