We present experimental results of the anomalous diffusion in a membrane system obtained by means of the laser interferometric technique. We show that in membrane system with glucose diffusing in a gel medium, the thickness of the concentration boundary layers manifest a subdiffusive character. Namely, the thickness of the concentration boundary layer \delta scales as t^\gamma with \gamma =0.443\pm 0.019.

PACS numbers: 05.60.Cd, 66.10.Cb, 82.65.Fr