A composite polymeric scaffold of gelatin/alginate /graphene is fabricated through freeze-drying technique. Initially, a hydrogel system comprised of gelatin/alginate (1:1) is prepared, and then the effect of different amounts of graphene carboxyl nanosheets (1,1.5, 2, and 2.5 wt.%) on the resultant structural properties are thoroughly evaluated. The swelling ratio, biodegradability, electrical and mechanical properties of bio-composite hydrogels are controlled by manipulating the concentration of graphene-COOH. The significant increase in the electrical conductivity is observed with the addition of 2.5% graphene-COOH, and the electrical conductivity increased from 8.525 x 10-7 +/- 0.01 S cm-1 to 7.644 x 10-4 +/- 0.04 S cm-1. Also, the biocomposite hydrogels exhibited compressive and tensile strength ranging from 25 to 382 KPa and 11.4 to 148 KPa with an increase in the concentration of graphene-COOH. The simplicity, low cost, tunable mechanical properties, and optimal electrical conductivity of the hydrogel system presented in this study highlight its potential as nerve tissue replacement.