In quasi-synchronous frequency-hopping multiple-access systems where relative delays between different users are restricted within a zone around the origin, low-hit-zone frequency-hopping sequences (LHZ-FHSs) are employed as spreading sequences. In this paper, we study LHZ-FHS sets obtained from the Cartesian product of some FHS sets. We first derive an upper bound on the Hamming correlation of FHSs constructed by the Cartesian product. We also give a general method to construct LHZ-FHS sets by the Cartesian product. We then present four new classes of optimal LHZ-FHS sets. The first three classes of sets are obtained from the product of Solomon's FHS sets and Kumar's FHS sets. The last one is constructed by the product of FHS sets based on interleaving techniques. These LHZ-FHS sets have new parameters not covered in the literature.