• A simple fabrication technique is introduced to create microhourglass-shaped channels. • Dimensional design factors are investigated to control the curvature of 3D geometries. • A tubular microchannel network with various sizes and shapes is fabricated. • The engineering of a blood vessel-like network is demonstrated by HLMECs culture. This paper describes an innovative yet straightforward fabrication technique to create three-dimensional microstructures with controllable tapered geometries by combining conventional photolithography and thermal reflow of photoresist. Positive photoresist-based microchannel structures with varying width-to-length ratios were reflowed after their fabrication to generate three-dimensional funnel structures with varying curvatures. A polydimethylsiloxane hourglass-shaped microchannel array was next cast on these photoresist structures, and primary human lung microvascular endothelial cells were cultured in the device to engineer an artificial capillary network. Our work demonstrates that this cost-effective and straightforward fabrication technique has great potential in engineering three-dimensional microstructures for biomedical and biotechnological applications such as blood vessel regeneration strategies, drug screening for vascular diseases, microcolumns for bioseparation, and other fluid dynamic studies at microscale. [ABSTRACT FROM AUTHOR]