Systematic calculations on the spectroscopy and transition properties of even-even Te isotopes are carried out by using the large-scale shell-model configuration-interaction approach with a realistic interaction. These nuclei are of particular interest since their yrast spectra show a vibrational-like equally spaced pattern whereas the few known E2 transitions show rotational-like behavior. This cannot be explained by available collective models. My calculations reproduce well the equally spaced spectra of those isotopes as well as the constant behavior for the B(E2) values of Te-114. The calculated B(E2) values of neutron-deficient and heavier Te isotopes show contrasting different behaviors along the yrast line. The B(E2) of light isotopes can exhibit a nearly constant behavior up to high spins. It is shown that this is related to the enhanced neutron-proton correlation when approaching N = 50.