Multiband and broadband metamaterial absorbers have been proposed in the paper. The proposed absorbers are composed of metallic copper patterns on both sides of a dielectric layer. One side consists of metallic circular patches and metallic annular patches, and the other side is of metallic ground plane. Each distinct metallic circular patch unit cell or annular patch unit cell has one distinct resonant peak in a very narrow band, and these unit cells are independent of one an other. Therefore, combining two different unit cells which resonates at different frequencies can obtain dual-band absorber. Based on the theory, combining three different unit cells can obtain tri-band absorber, and combining four different unit cells can obtain the absorber which resonates at four different frequencies. In addition, the electric field distribution verifies that each distinct unit cell resonates at a different frequency. Broadband metamaterial absorber can be obtained according to the optimized combination of the different unit cells. Increasing the number of different unit cells broadens the frequency range when their resonances are closely packed together, thereby resulting in a broadband resonance.