The electronic structures of Hf1-xZrxS3 and Hf1-xZrxSe3 trichalcogenides are investigated by first-principles calculation. In particular, step change of Zr concentration is intensively investigated. Our calculations reveal that doping of Zr atoms increase the strength of cohesion between the atoms in HfX3 (X = S, Se) monolayers, and results in occurring of energetically more stable alloys. In addition, doping of Zr atoms in HfS3 causes band gap bowing, which means the curve of band gap values shows quadratic nonlinearities while change from semimetal to semiconductor is observed in HfSe3 case. The examined band structures indicate that Hf1-xZrxS3 monolayers have very suitable band gap values for water splitting and also their band edge potentials have sufficiently higher or lower positions than the required potential values for the reduction or oxidation potentials.