Epsilon-near-mu metamaterials play a significant role in many fields such as radar, communication, and stealth technology, due to their ideal transmission responses. However, when electromagnetic (EM) waves illuminate such metamaterials at large angles, undesired reflectance occurs that greatly restricts the applications. Here, we propose a theoretical approach that can fundamentally eliminate the adverse effects of the incident angle on the transmission response of an anisotropic ε-near-μ material by adjusting the structural permittivity and permeability tensors. We take advantages of the nonresonance regions of electric and magnetic resonators so that the material parameters can attain the desired values in a wide frequency band. This allows us to design a nonreflective material with broadband all-angle transmissions from 0° to almost 90°, which is further verified by experiments with good performance. This work opens up a new route for the design of ultrawide-angle transmission-type metamaterials with high-efficiency and wideband properties, reaching significant applications in antenna radomes.