A polarization-insensitive and angle-independent graphene absorber (GA) with periodically patterned grating is demonstrated. A periodic nanocavity composed of multilayer subwavelength grating and metal substrate supports a strongly localized mode inside the cavity, where the mode helps to absorb more electromagnetic waves. The proposed GA exhibits polarization-insensitive behavior and maintains the high absorption above 90% within a wide range of incident angle (more than 80°). We attribute the high absorption to the excitation of the cavity mode resonance and magnetic resonance for the transverse electric and transverse magnetic polarizations, respectively. The proposed GA has potential applications in the design of various devices, such as optical modulators or tunable absorption filters because of its remarkable angle-insensitive absorption performance.