The reversible nonlinear conduction (RNC) behavior of high-density polyethylene/graphite powder composites with various graphite powder volume concentrations slightly above the threshold has been studied. The relationships between the current density (J) and electric field (E) of the composites, as shown in J(E) curves, can be well described by the scaling functions of J/J(c) similar to (E/E-c)(alpha1) when E < E-c and J/J(c) similar to (E/E-c)(alpha2) when E > E-c, where J(c) is the crossover current density and E-c is the crossover electric field. The results indicate that J scales with the linear conductivity sigma (o) as J(c) similar to o(o)(x). It is believed that the macroscopic RNC is a combined result of the microscopic conduction processes, involving electronic transporting along carbon chains and tunneling or hopping across thin polymer bridges.