Molecular dynamics simulations have been performed to study structural relaxation in the Zr67Ni33 alloy with pair functional potential. The time and space correlation of atoms are analyzed in real and reciprocal space for equilibrium liquid, supercooled liquid and amorphous state. The thermodynamically determined glass transition temperature is also characterized by the van Hove real-space correlation function. The details of atom motion in the amorphous state are analyzed using graphics of the atom trajectories. The cooperative jump motion and the slow translational motion are observed as minor motion in the amorphous state. The relaxation of the incoherent intermediate structure factor clearly reveals two relaxation processes below the melting point. The slow (α) relaxation is described by the stretched exponential function. The relaxation time shows non-Arrhenius type temperature dependence. The index increases with temperature. The fast (β) relaxation is fitted by the Debye type exponential function. For the equilibrium liquid state, the relaxation times of the α and β relaxations are of the same order. Therefore the relaxation is detected as one process.