In this paper, a broadband metamaterial absorber is designed based on a hybrid substrate consisting of the dielectric and magnetic materials. The absorber is composed of the resistance film, dielectric layer, magnetic layer, and metal backboard. Numerical simulation of the absorbing properties is performed by means of the finite-difference time-domain method, and the bandwidth of the reflectivity below -10 dB is optimized by the genetic algorithm. Simulated results indicate that a bandwidth of reflectivity below -10 dB can be achieved over the frequency range from 7.8 to 18 GHz when the thickness of the absorber is only 2.5 mm. The proposed metamaterial absorber has many advantages, such as thin thickness, broadband, and polarization insensitivity. The operation mechanism of the absorber has also been analyzed and discussed within the model of equivalent circuit. In the end, an absorber sample is fabricated based on the design. It is found that the experimental result is well consistent with the design requirements.