The pressure effect on the frustrated magnetic system CuFeO2 exhibiting multiferroic behavior has been studied by means of time-of-flight single crystal neutron diffraction combined with a hybrid-anvil-type pressure cell. The nonpolar collinear magnetic ground state (CM1 phase) with propagation vector k = (0, 1/2, 1/2) turns into a proper screw magnetic ordering with incommensurate modulation k = (0, q, 1/2; q similar or equal to 0.4) and a polar 21 ' magnetic point group (ICM2 phase), between 3 and 4 GPa. This spin structure is similar to the ferroelectric phase induced by magnetic field or chemical doping under ambient pressure. Above, 4 GPa, a magnetic phase (ICM3) appears, with an incommensurate propagation vector that is unique for the CuFeO2 system, k = (qa, qb, qc; qa similar or equal to 0, qb similar or equal to 0.34, qc similar or equal to 0.43). This propagation vector at the general point results in triclinic magnetic symmetry which implies an admixture of both cycloidal and proper screw spin configurations. The ICM3 phase is stable in a narrow pressure range, and above 6 GPa, the spin-density collinear structure (ICM1 phase), similar to the first ordered state at ambient pressure, takes place. Comparing the degree of lattice distortions among the magnetic phases observed at ambient pressure, we discuss the origin of the pressure-induced magnetic phase transitions in CuFeO2.