To reduce the complexity of the infrared optical system effectively while increasing the field of view of a panoramic imaging system, a catadioptric optical structure is used and a diffractive surface is introduced through reasonable rationing of the mirror and lens focal power. A catadioptric once-imaging uncooled infrared panoramic imaging optical system with the field of view up to 360°×(from -40° to 50°) and a catadioptric secondary imaging uncooled infrared panoramic imaging system with the field of view up to 360°×(from -30° to 50°) are designed respectively. The imaging system operates in the waveband from 8 m to 12 μm and its F number is 1.2. It can implement staring imaging at a certain pitch angle in a 360-degree viewing range. The design results show that the system is simple and compact in structure, large in posterior intercept and good in imaging quality. Its modulation transfer function value at the special frequency of 20 lp/mm is greater than 0.4, which can meet the application requirements.