Laser direct writing (LDW) is a promising candidate for the fabrication of all-dielectric THz absorbers for its high flexibility and material compatibility. However, multi-step processing or multi-layer materials are required to compensate for the nonideal features of LDW to realize good absorption performance. To further explore the potential of LDW in flexible and cost-effective THz absorber fabrication, in this work, we demonstrate a design method of THz absorbers fully considering and utilizing the characteristics of laser processing. Specifically, we first numerically analyze that by properly combining basic structures processed by single-step LDW, good and adjustable absorption performance can be achieved on a single-layer substrate. Then we experimentally fabricate THz absorbers by processing periodic composite structures, which are combined by grooves and circular holes, on single-layer doped silicon using LDW. Experimental results show that our method can fabricate THz absorbers at a speed of 3.3 mm2/min with an absorptivity above 90% over a broadband of 1.8-3 THz. Our method provides a promising solution for the flexible and efficient fabrication of all-dielectric broadband THz absorbers.