Based on the recently constructed Ni-Zr-Al n-body potential, Monte Carlo simulations are performed to study the glass formation and associated structural evolutions in the system. The micro-chemical inhomogeneity (MCI) parameter and Honeycutt and Anderson (HA) pair analysis are employed to investigate both the chemical short-range orders and topological short-range orders for the ternary Ni-Zr-Al metallic glasses. Results reveal that remarkable chemical short-range orders (CSROs) exist in the ternary Ni-Zr-Al metallic glasses and are strongly influenced by the chemical interactions among the constituent elements. Moreover, topological short-range orders are clearly formed in the ternary Ni-Zr-Al metallic glasses, with the most remarkable characteristic being the icosahedral local packing. Similarly to CSRO, the extent of icosahedral short-range orders formed in the Ni-Zr-Al system varies distinctly with the chemical composition. In addition, simulation results reveal that chemical short-range orders and topological short-range orders turn out to be influenced by different factors. Unlike CSRO, both chemical interactions and geometrical constraints play important roles in forming the topological short-range orders.