Incident-angle-dependent wavefront manipulation, especially in transmission, is highly desired in the realm of electromagnetic waves. In this work, we demonstrate a unique type of angle-dependent multifunctional metasurfaces (ADMMs) that exhibit distinct wavefront control functionalities under illumination at different incident angles. The ADMMs are composed of two kinds of transmissive meta-atoms, which have identical transmission phases under normal incidence, but π-phase difference under the oblique incidence at 60°. Such a distinguished transmission phase difference stems from the opposite angular dispersion properties of the two meta-atoms. By arranging these two kinds of meta-atoms randomly, the transmission wavefront can be efficiently diffused under oblique incidence. However, the transmission wavefront is invariant under normal incidence regardless of the arrangement of the meta-atoms. This functionality is verified by both numerical simulations and microwave experiments, which show strong agreement with each other. Our finding paves a road toward incident-angle-dependent wave-diffusing devices, which have potential applications in wireless communications and angular dispersive devices.