A new scheme of asymmetric elliptic-cone-shaped microlens (AECSM) employing a single-step fabrication technique for efficient coupling between the high-power 980-nm laser diodes and the single-mode fibers is proposed. The AECSMs are fabricated by asymmetrically shaping the fiber during the single-step grinding process and elliptically lensing the fiber tip during the fusing process. A maximum coupling efficiency of 85% and a high-average coupling efficiency of 71% have been demonstrated for a 980-nm laser diode with a high aspect ratio of 5. 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. Therefore, this AECSM can form different aspect ratios of asymmetric elliptical microlenses to match the far field of the high-power diode lasers that is suitable for use in commercial high-power pump laser modules.