Studying the real-time dynamics of strongly correlated systems poses significant challenges, which have recently become more manageable thanks to advances in density matrix renormalization group (DMRG) and tensor network methods. A notable development in this area is the introduction of a complex-time evolution scheme for tensor network states, originally suggested for solving Anderson impurity model and designed to suppress the growth of entanglement under time evolution. In this study, we employ the complex-time evolution scheme to investigate 1) the dynamics of one-dimensional spin systems and 2) the spectral properties of multi-orbital Anderson impurity models for application to the dynamical mean-field theory. In the spin model case, we study the dynamic critical exponent of the transverse-field Ising model and the dynamical structure factor of the XXZ model across the gapped and gapless phases. In the Anderson impurity model case, we employ a fork tensor network model and obtain self-energies directly in the real-frequency domain, which enables obtaining high-energy features in the spectral functions of several systems like SrVO3 and CuV2S4. In both cases, complex-time evolution reproduces the results of real-time evolution while mitigating the rapid growth of quantum entanglement typically associated with the latter, providing a robust and efficient framework for studying the dynamics of correlated quantum systems. Lastly, we introduce our recent effort to better extrapolate the computed data in the time domain.