The effects that the catalyst-to-feed ratio have on the yields of products and composition of the naphtha and light cycle oil (LCO) fractions in the hydrocracking of a blend composed of high-density polyethylene (HDPE) and vacuum gasoil (VGO) using a PtPd/HY catalyst were assessed. The hydrocracking runs were carried out in a batch reactor fixing the following operation conditions: 420 °C, 80 bar, 120 min and an HDPE-to-VGO ratio of 0.2 gHDPE gVGO−1, varying the catalyst-to-feed mass ratio within the 0.05–0.1 gcatalyst gfeed−1 range. The obtained results exposed that a catalyst-to-feed mass ratio of 0.075 gcatalyst gfeed−1 provided the best results, since the conversion of the heavy cycle oil (HCO) fraction and of the HDPE offered quite high values (73.1 and 63.9%, respectively) without causing an excessive overcracking in the form of gas products (the yield of gases was of 25%). Moreover, an interesting yield of naphtha (37.0 wt%) with an RON within the commercial standards (92.5) was obtained. With regard to coke formation, not-so-developed structures were formed for a catalyst-to-feed mass ratio of 0.075 gcatalyst gfeed−1, easing their combustion and presumably extending the lifespan of the catalyst.