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A new design approach for achieving quadband terahertz metamaterial absorber, formed by an asymmetric resonator and a metallic board separated by a certain thickness dielectric layer, is numerically studied and demonstrated. Results show that the absorber has four high absorption (greater than 98%) resonance bands (or peaks). The physical origin of the absorber is attributed to four different resonance modes of the single-patterned resonator. The proposed device resolves large unit size, complex resonance structure, and time-consuming and costly fabrication steps, which previously reported absorbers frequently encountered. Moreover, the five-band metamaterial absorber can be obtained by further optimizing the parameters of resonator. The proposed absorber has application prospects in many areas such as materials detection, thermal imaging, and biological sensing.