The nonlinear response in high-density polyethylene/graphite nanosheets conducting composites under increasing applied voltage is investigated. Under sufficient applied constant voltage, the resistance increases initially due to Joule heating effect and then eventually reaches a steady value with a characteristic thermal relaxation time tau(h) , which decreases as the applied field increases. The switch value, namely the ratio of the resistance under steady condition to the resistance of sample in linear regime, gradually increases with the increasing applied field. The threshold voltage (V (0)) at which the resistance start to increase with time scales with linear regime resistance (R (0)) of the sample as V-0 similar to R-0(x), with the exponent x = 0.78 +/- 0.05. All the curves of R/R-0 vs. V/V-0 collapse to a similar curve with the function R/R-0 = 1 + alpha(V/V-0)(theta). The results reveal that the threshold voltage value decreases with increasing graphite nanosheets content in the composites.