This paper presents a lightweight microwave absorber suitable for space applications. The absorber is based on a resistive high-impedance surface (RHIS) optimized to achieve reflection under −15 dB in the band (2-2.3 GHz) at oblique incidence for transverse electric (TE) and transverse magnetic (TM) polarizations. A first classical isotropic RHIS structure is shown to be limited to angles of incidence up to 40° for TE polarized waves and up to 35° for TM polarized waves. So the objective of this contribution is to present a second solution based on an anisotropic RHIS structure which presents good absorption of incident waves in TE and TM polarizations for larger angles of incidence. An example is presented for an incidence angle of 65°.