In this work, for the first time, naphthalene (NA)-based polymers were synthesized by one-stage Friedel–Crafts crosslinking. The influence of NA functionalization by -OH, -SO3H, and -NO2groups on the polymers’ porosity and distribution of the catalytically active phase (Pd) was studied. Synthesized catalytic systems containing 1 wt.% of Pd either in the form of Pd(II) species or Pd(0) nanoparticles supported on NA-based polymers were tested in a model reaction of Suzuki cross-coupling between 4-bromoanisole and phenylboronic acid under mild reaction conditions (60 °C, ethanol-water mixture as a solvent). These novel catalysts demonstrated high efficiency with more than 95% of 4-bromoanisole conversion and high selectivity (>97%) for the target 4-methoxybiphenyl.