To analyze the infrared signatures of plumes, an improved coupled infrared radiation model is proposed based on the spherical harmonic discrete coordinate method (SHDOM) and the computational fluid dynamics (CFD) technique. We simulate the temperature field, pressure field and medium composition distribution information of the plume, and apply the information of flow field as the input data to calculate real radiation properties of the plume. The absorption coefficients of different plumes are calculated by the Weight-Sum-of-Gray-Gas (WSGG) algorithm. In addition, using the statistical average scattering phase function of particle clusters, the effect of Al2O3 on the total radiation is considered, which overcomes the inaccurate description of the multiple scattering source function of particles in the traditional SHDOM and makes it suitable for solving the infrared radiation problem of plumes. Multiple scattering, emission, and absorption processes between the alumina particles and the gases are considered rigorously. The infrared radiation signatures along different detection directions of rocket plumes with various velocities and wavebands are simulated, of which the validity is verified through the signature comparison with the Standardized Infrared Radiation Model (SIRRM). Numerical results show that the effect of aluminum particle clusters on the infrared radiation characteristics of rocket plumes cannot be neglected, especially for wavebands at which the absorption of gas molecules is weak. Moreover, the contribution of aluminum particles to the total radiation is related to the zenith angle and wave band, which indicates the importance and necessity of considering the aluminum particle clusters.