Graphene (Gr) distribution in low-density polyethylene (LDPE) considerably increased thermal stability, thermal conductivity, mechanical properties, and flexural properties of LDPE/Gr composites. Addition of Grs to LDPE postponed the time for making the polymer brittle. High specific surface area and superior properties of Gr improved thermal stability, conductivity, storage modulus, and mechanical properties of composites. The electrical conductivity of LDPE/Grs composites upgraded owing to the thermal stability of Grs in LDPE matrix. In terms of rheology, the addition of Grs augmented viscosity of the LDPE matrix. Addition of Grs to LDPE nucleates crystallization by reducing the activation energy along with rising crystallization onset temperature. Adding Gr facilitated decreasing aggregation, expanded crystallinity, improved the local lattice order of LDPE/Grs, and advanced Grs contact with LDPE. Thus, on a macroscopic scale, Gr constrains mobility of polymer chains, causing a growth in stiffness and strength of the composite. The distribution of Grs in LDPE at micron size scale was verified by atomic force microscopy and other microscopic testers. With further Grs inclusions to LDPE, the activation energy reduced, Grs proceeded as nucleating agents throughout the crystallization of composites, and increased the enhancement of relative crystallinity of LDPE/Gr compounds. The percolation phenomenon of LDPE/Gr composite occurred about 0.5 wt of Gr loading. Due to further addition of Gr to LDPE, the impermeability of oxygen through the conduit raised somehow the LDPE/Gr sample with 0.5 wt Gr content, generated a sharp improvement, and dropped fuel permeation with about 37 in comparison with pure LDPE. © The Author(s) 2018.