Rapid radiative transfer models are crucial to remote sensing and data assimilation. An integrated efficient radiative transfer model named Dayu, which is an updated version of the Efficient Radiative Transfer Model (ERTM) is developed to simulate the imager measurements in cloudy atmospheres. In Dayu model, the Optimized alternate Mapping Correlated K-Distribution model (OMCKD) which is predominant in dealing with the overlap of multiple gaseous lines is employed to efficiently calculate the gaseous absorption. The cloud and aerosol optical properties are pre-calculated and parameterized by the particle effective radius or length. Specifically, the ice crystal model is assumed as a solid hexagonal column, of which the parameters are determined based on massive aircraft observations. For the radiative transfer solver, the original 4-stream Discrete ordinate aDding Approximation (4-DDA) is extended to 2N-DDA (2N is the number of streams) which can calculate not only the azimuthally dependent radiance in the solar spectrum (including solar and infrared spectra overlap) but also the azimuthally averaged radiance in the thermal infrared spectrum through a unified adding method. Then the accuracy and efficiency of Dayu model are evaluated by comparing it with the benchmark model, i.e., Line-By-Line Radiative Transfer Model (LBLRTM) and DIScrete Ordinate Radiative Transfer (DISORT). Under the standard atmospheric profile, the maximum relative biases between Dayu model with 8-DDA / 16-DDA and the benchmark model (OMCKD with 64-stream DISORT) are 7.63% / 2.62% at solar channels but decreased to 2.66% / 1.39% at spectra-overlapping channel (3.7 μm). The computational efficiency of Dayu model with 8-DDA / 16-DDA is approximately three / two orders of magnitude higher than that of the benchmark model. At thermal infrared channels, the brightness temperature (BT) differences between Dayu model with 4-DDA and the benchmark model (LBLRTM with 64-stream DISORT) are bounded by 0.65K. Compared to the benchmark model, Dayu model with 4-DDA improves the computational efficiency by five orders of magnitude. In the application to the practical Typhoon Lekima case, the simulated reflectances and BTs by Dayu model have a high consistency with the imager measurements, demonstrating the superior performance of Dayu model in satellite simulation.