Albedo may be derived from clear-sky remote-sensing images through inversion of a bidirectional reflectance distribution function (BRDF) model and angular integration. This paper proposes a new multi-angular and multi-spectral BRDF model (ASK Model) based on the kernel-driven conception and gives an effective algorithm for broadband albedo retrieval. By adding component spectra into kernels as prior known driven variables, the new model expresses BRDF as a linear combination of wavelength-independent kernel coefficients and kernels expressed as functions of both observation geometry and wavelength. In this way, the new model brings advantages in two aspects. On the one hand, for model inversion, the new angular and spectral kernels allow combination of observations not only at different viewing and illumination angles, but also at different wavebands, which give more reliable inversion results especially when the angular data are limited. On the other hand, different from traditional narrowband-to-broadband conversion, which gives empirical weights at several available bands, the new algorithm derives broadband albedo as a weighted linear combination of kernel integrations both in angular and wavelength domains. As model validation, ground-based measurements in Heihe Field Campaign have been chosen. Results show that the new model can accurately rebuild BRDF and derive broadband albedo. Furthermore, the new model and algorithm are demonstrated using CHRIS and EOS-MODIS data. The retrieved broadband albedos have been compared with MODIS BRDF/albedo product and the in situ measurements. Results show that the presented algorithm can be employed to retrieve broadband albedo from multisource satellite observations.