Understanding of domain wall (DW) propagation in a complex structure is an essential first step toward the development of any magnetic-domain based devices including spin-based logic or magnetic memristors. Interfacial Dzyaloshinskii-Moriya interaction (iDMI) in the structure with broken inversion symmetry induces an asymmetrical DW configuration with respect to the direction of in-plane field. Dynamic behaviors of field-driven DW within the film with perpendicular magnetic anisotropy is influenced by DW tilt from the iDMI effect and the corners in the T-shaped structure of the DW path. Images from Kerr microscopy reveal that the iDMI effective field contributes to a tilted structure of DW configuration and evolution along its propagation. With the combination of iDMI and T-shaped structure, we observed two distinguished bidirectional DW propagations in two output branches and distinct arriving times at the destination pads with a uniform external field. Micromagnetic simulation results is compared with the observed dynamics of a DW configuration in the structure providing an additional confirmation of the interpreted results.