Summary: The relation \(\prec\) on the usual direct product \(\prod_{i \in I}L_i\) of a family of molecular lattices \(\{L_i\}_{i \in I}\) is introduced by means of the relation \(\triangleleft\) on complete lattices. Some fundamental properties of the relation \(\prec\) are discussed. Based on the relation \(\prec\), the concept of the \(\prec\)- lower sets on the direct product \(\prod_{i \in I}L_i\) is given, and it is proved that the set of all \(\prec\)- lower sets on the direct product \(\prod_{i \in I} L_i\) forms a molecular lattice. Hence, the product structure of a family of molecular lattices in the category of molecular lattices is obtained, and all molecules and complete molecules in the product object are given. It is finally proved that the product object of a family of strong molecular lattices in the category of molecular lattices is also a strong molecular lattice.