We report a simple, low-cost, rapid, and mask-free method to fabricate two-dimensional (2D) and three-dimensional (3D) microfluidic chip for biological analysis researches. In this fabrication process, a laser system is used to cut through paper to form intricate patterns and differently configured channels for specific purposes. Bonded with cyanoacrylate-based resin, the prepared paper sheet is sandwiched between glass slides (hydrophilic) or polymer-based plates (hydrophobic) to obtain a multilayer structure. In order to examine the chip's biocompatibility and applicability, protein concentration was measured while DNA capillary electrophoresis was carried out, and both of them show positive results. With the utilization of direct laser cutting and one-step gas-sacrificing techniques, the whole fabrication processes for complicated 2D and 3D microfluidic devices are shorten into several minutes which make it a good alternative of poly(dimethylsiloxane) microfluidic chips used in biological analysis researches.