A new scheme of asymmetric elliptic-cone-shaped microlens (AECSM) employing a single-step fabrication technique for efficient coupling between the high-power 980nm laser diodes and the single-mode fibers is proposed. The asymmetric elliptic-cone-shaped fiber endface (AECSFE) was fabricated by a single-step grinding and polishing a cleaved fiber by applying a periodically variable torque on the fiber ferrule to change the grinding pressure. The periodically variable torque was made by an eccentric mass with a constant rotation speed double that of the fiber. After the AECSFE was formed, an AECSM was obtained by heating the fiber tip in a fusing splicer. In comparison with the previous works on asymmetric fiber microlenses fabricated by the multi-step processes with complicated fabrication, the advantages of the AECSM structure for achieving high coupling are a single-step fabrication, a reproducible process, and a high-yield output. In this study, we demonstrated that the average grinding offset of the AECSM structure for 30 measurements was about 0.4 £gm, the average coupling efficiency was 71%, and the maximum of the measured coupling efficiency was 83%. The yield of the AECSM for coupling efficiency over 70% was 47%, for coupling efficiency over 60% was almost 100%.