This thesis is concerned with the application of the time-dependent density functional theory (TDDFT) to investigate the fission dynamics of atomic nucleus, which is still one of the most complicated problem in nuclear physics and a full microscopic interpretation is still missing. The establishment of the time-dependent superfluid local density approximation (TDSLDA) and the increasing power of computing resources make the three-dimensional symmetry unrestricted simulations of fission dynamics possible in recent years. In this work, a qualitative new nuclear energy density functional (NEDF) is developed, which contains only seven uncorrelated fitting parameters, and have excellent performance in describing various nuclear properties, e.g. nuclear mass, charge radii, neutron separation energy, shell structure, and deformation properties like the height of fission barriers and the excitation energy of fission isomer. Using such NEDF and another popular NEDF among fission practitioners, SkM*, a comprehensive study of fission dynamics with TDSLDA formalism is presented. The role of pairing correlations in fission dynamics is demonstrated quantitatively. It is also shown that independent TDSLDA trajectories with different initial conditions on the potential energy surface generate almost the same fission fragment (FF) configurations, e.g. the mass split, total kinetic energy, total excitation energies etc. An important aspect of this study is to provide a quantitative validation that the fission dynamics from saddle to scission is a non-adiabatic, overdamped one. To overcome the limitation of TDDFT that fails to produce the variances in the FF properties, a novel method in the spirit of the classical Langevin approach is promoted to include fluctuations and dissipations into the TDDFT framework. Promising results are obtained in a simpler nuclear hydrodynamics simulation, while its implementation in full TDSLDA calculation is still challenging.