This paper presents the design considerations, the simulation results and the test results for a new type S-band high-average-power broadband klystron. In this paper, a method which is used for verifying the quality of an electron-optics-system of a high-average-power broadband klystron is proposed. And then the coordinate method using the 2.5D Arsenal-MSN code and the KLY6 code is also described, which deals with eliminating the potential output-power-sag and optimizing the parameters of the RF-interaction region for broadband klystrons. The further hot-test results prove that both of the methods are effective.