A nanocomplex of Chromium oxide nanoparticles with biopolymer matrix of gum Arabica is synthesized by natural self-assembly in chemical sol-gel route. Gum Arabica is chosen as base matrix due to its inherent biodegradable property. Experimental specimen of the said complex is prepared to satisfy near quantum size effect criterion. Due to near quantum size effect and spatial localization of nanoclusters, the developed specimen becomes an ideal 2D quantum well system. The longitudinal electrical conduction of the developed system is studied experimentally. Some of its structural aspects are also investigated to make the study conclusive. The dispersed cluster size is estimated by Transmission Electron Microscope (TEM) and X-ray diffraction (XRD). The results of I-V characteristics at temperatures 253 K show the distinctive features of localized energy levels. The spacing between energy levels near ground state to be comparable to the thermal energy at temperature 253 K for a cluster dimension below 10 nm. In this present study the developed specimens with the mentioned nanoclusters estimated from TEM and XRD as below 10 nm. The overall results are found to be encouraging.