First-principles calculations have been carried out to study the InVO4 compound under pressure. In this work, total energy calculations were performed in order to analyze the structural behavior of the experimentally known polymorphs of InVO4: alpha-MnMoO4-type (I), CrVO4-type (III), and wolframite (V). In addition, in this paper we present our results about the stability of this compound beyond the pressures reached by experiments. We propose some new high-pressure phases on the basis of the study of 13 possible candidates. The quasi-harmonic approximation has been used to calculate the sequence of phase transitions at 300 K: CrVO4-type, III (the transition pressure is given in parentheses)-> wolframite, V (4.4 GPa)-> raspite, VI (28.1 GPa) -> AgMnO4-type, VII (44 GPa). Equations of state and phonon frequencies as a function of pressure have been calculated for the studied phases. In order to determine the stability of each phase, we also report the phonon dispersion along the Brillouin zone and the phonon density of states for the most stable polymorphs. Finally, the electronic band structure for the low- and high-pressure phases for the studied polymorphs is presented as well as the pressure evolution of the band gap by using the HSE06 hybrid functional.