Cooper-pair density modulation (CPDM) states are superconducting phases in which the order parameter varies periodically in real space without breaking translational symmetry1–3. Moiré superlattices in layered materials4–18 have recently emerged as powerful platforms for engineering charge density with tunable lattice symmetry, offering a new route to creating and controlling CPDM states. Here we demonstrate moiré-induced CPDM states in a bilayer heterostructure formed by epitaxially stacking one quintuple layer (1QL) of topological insulator Sb2Te3 on a six-unit-cell (6UC) antiferromagnetic FeTe layer. Scanning tunnelling microscopy and spectroscopy (STM/S) measurements reveal a moiré superlattice formed between the hexagonal tellurium lattice of Sb2Te3 and the square tellurium lattice of FeTe, which spatially modulates the two superconducting gaps of the 1QL Sb2Te3/6UC FeTe bilayer. Our Josephson STM/S measurements provide direct real-space imaging of the CPDM states with a wavelength corresponding to the periodicity of the moiré superlattice. By substituting Sb2Te3 with Bi2Te3, we achieve control over both the periodicity and magnitude of the CPDM states. Our work demonstrates an epitaxial strategy for synthesizing moiré superlattices from materials with different crystal symmetries and reveals a new mechanism for engineering CPDM states in designer bilayer heterostructures.