When the rocket engine is working in high vacuum environment, the gas jet expands rapidly under the condition of extremely low back pressure, forming the vacuum plume. This vacuum plume can produce impact and erosion on space targets, and its infrared radiation characteristics can be widely used for the detection and recognition of the space targets. Based on the theoretical model of collisionless free molecular flow, the rapid analytical calculation of vacuum plume was carried out in this paper. The expansion and diffusion characteristics of the plume were obtained, which accorded with the known flow rule. On the basis of the calculated plume flow parameters, the Voigt line function was used to describe the dilating of the rarefied gas, and the radiation characteristics were calculated by line-by-line and LOS method. The results show that the boundary and diffusion distribution of vacuum plume are determined by the speed ratio of the nozzle exit. The stronger exit speed ratio is, the greater the area of the plume diffusions, and the higher the normalized density and temperature on the axis are. When the temperature of the nozzle exit is same, the radiation intensity of the plume increases with the increase of exit speed ratio. However, when the speed of the nozzle is same, the radiation intensity of the plume decreases with the increase of exit speed ratio. In the case of the same exit speed ratio, the radiation intensity is positively correlated with the thrust.