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Geotextiles are excellent anti-filtration materials commonly used in the field of water conservancy engineering; however, the factors affecting the water permeability performance of geotextiles under stressed states during operation have not been fully identified. To investigate the effect of unidirectional stretching on the water permeability of geotextiles, a unidirectional rheological head infiltration test was conducted on the geotextiles using a self-developed test apparatus. In addition, the water permeability of geotextiles with different thicknesses and tensile states was calculated using a set of water permeability calculation methods based on the nonlaminar flow state of geotextiles. The results showed that the water permeability of the W120 geotextile samples initially decreased and then increased under warp stretching and gradually increased under weft stretching. However, the water permeability of the W200 geotextile samples initially decreased and then increased under both warp and weft stretching. Therefore, the thickness of the geotextile affected its permeability properties.