Micro-droplets are widely used in the fields of chemical and biological research, such as drug delivery, material synthesis, point-of-care diagnostics, and digital PCR. Droplet-based microfluidics has many advantages, such as small reagent consumption, fast reaction time, and independent control of each droplet. Therefore, various micro-droplet generation methods have been proposed, including T-junction breakup, capillary flow-focusing, planar flow-focusing, step emulsification, and high aspect (height-to-width) ratio confinement. In this study, we propose a microfluidic device for generating monodisperse micro-droplets, the microfluidic channel of which has an asymmetric cross-sectional shape and high hypotenuse-to-width ratio (HTWR). It was fabricated using basic MEMS processes, such as photolithography, anisotropic wet etching of Si, and polydimethylsiloxane (PDMS) molding. Due to the geometric similarity of a Si channel and a PDMS mold, both of which were created through the anisotropic etching process of a single crystal Si, the microfluidic channel with the asymmetric cross-sectional shape and high HTWR was easily realized. The effects of HTWR of channels on the size and uniformity of generated micro-droplets were investigated. The monodisperse micro-droplets were generated as the HTWR of the asymmetric channel was over 3.5. In addition, it was found that the flow direction of the oil solution (continuous phase) affected the size of micro-droplets due to the asymmetric channel structures. Two kinds of monodisperse droplets with different sizes were successfully generated for a wider range of flow rates using the asymmetric channel structure in the developed microfluidic device.