(Lu1–xMnx)MnO3solid solutions, having the perovskite-type structure and Pnmaspace group, with 0 ≤ x≤ 0.4 were synthesized by a high-pressure, high-temperature method at 6 GPa and about 1670 K from Lu2O3and Mn2O3. Their crystal and magnetic structures were studied by neutron powder diffraction. The degree of octahedral MnO6tilting decreases in (Lu1–xMnx)MnO3with increasing x. Only the incommensurate (IC) spin structure with a propagation vector of k= (k0, 0, 0) and k0≈ 0.44 remains in (Lu0.9Mn0.1)MnO3in the whole temperature range below the Neel temperature TN= 36 K, and the commensurate noncollinear E-type structure that has been reported in the literature for undoped o-LuMnO3is not observed. (Lu1–xMnx)MnO3samples with 0.2 ≤ x≤ 0.4 have a ferrimagnetic structure with a propagation vector of k= (0, 0, 0) and ferromagnetic (FM) ordering of Mn3+and Mn4+cations at the B site, which are antiferromagnetically coupled to a noncollinear predominantly FM arrangement of Mn2+at the A site. The ferrimagnetic Curie temperature, TC, increases monotonically from 67 K for x= 0.2 to 118 K for x= 0.4. Magnetic and dielectric properties of (Lu1–xMnx)MnO3and a composition–temperature phase diagram are also reported.