Recent experiments showed the distinct observations on the transition metal ditelluride NiTe$_2$ under pressure: one reported a superconducting phase transition at 12 GPa, whereas another observed a sign reversal of Hall resistivity at 16 GPa without the appearance of superconductivity. To clarify the controversial experimental phenomena, we have carried out first-principles electronic structure calculations on the compressed NiTe$_2$ with structure searching and optimization. Our calculations show that the pressure can transform NiTe$_2$ from a layered P-3m1 phase to a cubic Pa-3 phase at $sim$10 GPa. Meanwhile, both the P-3m1 and Pa-3 phases possess nontrivial topological properties. The calculated superconducting $T_c$s for these two phases based on the electron-phonon coupling theory both approach 0 K. Further magnetic transport calculations reveal that the sign of Hall resistance for the Pa-3 phase is sensitive to the pressure and the charge doping, in contrast to the case of the P-3m1 phase. Our theoretical predictions on the compressed NiTe$_2$ wait for careful experimental examinations.
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