The correlation between the charge-order wave vector QCD and second-neighbor hopping t in cuprate superconductors is studied based on the t-t -J model. It is shown that the magnitude of the charge-order wave vector QCD increases with the increase of t , and then the experimentally observed differences of the magnitudes of the charge-order wave vector QCD among the different families of cuprate superconductors at the same doping concentration can be attributed to the different values of t .PACS numbers: 71.45. Lr, 71.18.+y, 74.72.Kf, 74.25.Jb, 74.20.Mn The charge-order correlation, as a competing phenomenon to superconductivity, is a common feature of cuprate superconductors 1-9 . In particular, the electron Fermi surface (EFS) measurements in the angleresolved photoemission spectroscopy (ARPES) experiments demonstrated a close connection between the charge-order wave vector Q CD and the wave vector connecting the tips of the Fermi arcs 1,2,6 , which in this case coincide with the hot spots on EFS, providing an evidence that the charge-order correlation is a natural consequence of the EFS instability. However, the magnitudes of the charge-order wave vector Q CD are different for the different families of cuprate superconductors at the same doping concentration 1-9 . In this case, a systematic investigation of the different magnitudes of the charge-order wave vectors among the different families of cuprate superconductors is useful for the understanding of the physical origin of the charge-order formation. Very soon after the discovery of superconductivity in cuprate superconductors, Anderson 10 argued that the essential physics of cuprate superconductors is contained in the t-J model on a square lattice, with t and J that are the nearest-neighbor hopping and nearest-neighbor spin-spin antiferromagnetic exchange, respectively. However, the experimental data detected from various techniques have introduced important constraints on the microscopic model [11][12][13][14][15] . In particular, the early ARPES experiments 13-15 indicated that the electronic structure and the related overall EFS in cuprate superconductors can be properly described only by generalizing the t-J model to include the second-and third-nearest neighbor hopping terms t and t . Furthermore, the experimental analysis 15 also showed that the superconducting transition temperature T c in the different families of cuprate superconductors is strongly correlated with t . However, it has been shown experimentally that the values of t and J are almost common for the different families of cuprate superconductors, and only the values of t and t are different [11][12][13][14][15] . In this case, a question is raised: is there a correlation between the experimentally observed differences of the magnitudes of the charge-order wave vector Q CD among the different families of cuprate superconductors at the same doping concentration and the second-nearest neighbor hopping t .In the recent studies, the nature of the charge-order correlation in cuprate superco...