Using molecular dynamics simulation with the embedded atom method, the structural properties of liquid NiAl in a pressure range of 0-20 GPa are investigated with a quenching rate of 2 K ps(-1). Not only is vitrification of liquid at low temperature detected, but also crystallization by change of average atomic volume as a function of temperature. Convincing evidence is presented that the applied pressure strongly affects the vitrification and crystallization of metallic liquid. The simulated glass transition temperature T(g) increases with pressure by 38.4 K GPa(-1) within the range 0-10 GPa, while external pressure induces crystallization of metallic liquid within the pressure range 10-20 GPa, and the crystallization temperature T(c) increases with a slope of 6.4 K GPa(-1). Therefore, the critical pressure for the formation of metallic glass at this cooling rate is estimated to be 10 GPa. The competition between the densification and the suppression of atomic diffusion in the liquid by pressure is able to explain the vitrification and crystallization behaviours of the liquid. Our present work provides a possible guidance for an experiment to study the pressure effect on the glass transition and crystallization process in metallic liquid.