Composites of insulating polyethylene and carbon black are widely used in switching elements, conductive paint, and other applications due to the large gap of resistance value. This research addresses the critical exponent of dielectric breakdown strength of polymer matrix composites (PMC) made with carbon black and polyethylene below the percolation threshold (Pt) for the first time. Here, Pt means the volume fraction of carbon black of which the resistance of the PMC is transferred from its sharp decrease to gradual decrease in accordance with the increase of carbon-black-filled content. First, the Pt is determined based on the critical exponents of resistivity and relative permittivity. Although huge cohesive bodies of carbon black are formed in case of being less than the Pt, a percolation path connecting the conducting phases is not formed. The dielectric breakdown strength (Dbs) of the PMC below Pt is measured by using an impulse voltage in the range from 10 kV to 40 kV to avoid the effect of joule heating. Although the observed Dbs data seems to be well fitted to a straight line with a slope of 0.9 on a double logarithm of (Pt-$V_{CB}$) and Dbs, the least squares method gives a slope of 0.97 for the PMC. It has been found that finite carbon-black clusters play an important role in dielectric breakdown.