EuFe2As2-based iron pnictides are quite interesting compounds, due to the two magnetic sublattices in them and the tunability to superconductors by chemical doping or application of external pressure. The effects of hydrostatic pressure on the static magnetism in Eu(Fe0.925Co0.075)2As2 are investigated by complementary electrical resistivity, ac magnetic susceptibility and single-crystal neutron diffraction measurements. A specific pressure-temperature (P-T) phase diagram of Eu(Fe0.925Co0.075)2As2 is established. The structural phase transition, as well as the spin-density-wave order of Fe sublattice, is suppressed gradually with increasing pressure and disappears completely above 2.0 GPa. In contrast, the magnetic order of Eu sublattice persists over the whole investigated pressure range up to 14 GPa, yet displaying a non-monotonic variation with pressure. With the increase of the hydrostatic pressure, the magnetic state of Eu evolves from the canted antiferromagnetic structure in the ground state, via a pure ferromagnetic structure under the intermediate pressure, finally to an "unconfirmed" antiferromagnetic structure under the high pressure. The strong ferromagnetism of Eu coexists with the pressure-induced superconductivity around 2 GPa. Comparisons between the P-T phase diagrams of Eu(Fe0.925Co0.075)2As2 and the parent compound EuFe2As2 were also made.