The time-dependent viscoelastic behaviors of an Low-Density-Pdyethyene(LDPE) (PE-FSB-23D022) melt were experimentally investigated using two types of thixotropy-loop test i.e., the triangular- and the trapezoidal-loop shear test. The shear strengthening was noted in the thixotropy-loop tests not only at high shear rate but also at low shear rate, and it was found that the dimensionless stress amplitude of shear strengthening at low shear rate is larger than that at high shear rate. Moreover, the shear strengthening is a time-dependent viscoelastic behavior that is observed during the initial stage of shearing, and it cannot be found when the time interval corresponding to the increase in shear rate is sufficiently long. The remarkable shear-weakening phenomenon was noticed at higher shear rate when shearing time is prolonged. Five types of the triangular thixotropy-loop results were marked in terms of the configurations of the stress-rate curves, which indicate the complex features of the time-dependent viscoelasticity. A simple model was used to describe the thixotropy-loop tests, and the fitted results showed good agreement with the experimental results.