Missiles and fighter jets that travel at a speed much higher than the speed of sound experience highly elevated temperatures due to air friction. Conventional anti-reflection coating designs based on heterogeneous materials may not be well suited to these applications as a variety of temperature-induced problems degrade the anti-reflection performance and the structural integrity. Here, authors show that a dielectric-based anisotropic metamaterial slab can serve as an effective, broadband anti-reflection layer for microwaves. The metamaterial is made of a single material, potentially the same material as the substrate, and contains (quasi-)periodic array of deep-subwavelength anisotropic voids. By controlling the aspect ratio and volume fraction of the voids, the anti-reflection property can be designed to be significantly better than that of an isotropic film especially in terms of suppression of reflection for wide angle range of incident beams. The spectral and angular performance of the design is presented based on accurate numerical analysis.