We study a geometrically anisotropic internal nano-layered structure of the shrunken multi-lamellar vesicle(SMLV) by using optical tweezers with a polarized beam. The SMLVs are synthesized from soybean asolectin by using gentle hydration method and has an optically birefringence property, known as a form birefringence. When a laser beam of optical tweezers with an elliptical polarization passes through the material with an optical birefringence, the ordinary and extraordinary components of the laser light experience different phase shift, respectively. Therefore, an optical torque due to the angular momentum conservation can be exerted on the optically birefringence material generating a rotational motion of the system. In this work we analyze the distance between the next bilayers of the membrane structure in SMLV from the experimentally measured data of the rotational motion and propose a simple model in which the SMLV is idealized as a multi-regularly-thin parallel plate structure.