The double perovskite CaMnTi2O6, is a rare A site ordered perovskite oxide that exhibits a sizable ferroelectric polarization and relatively high Curie temperature. Using first-principles calculations combined with detailed symmetry analyses, we identify the origin of the ferroelectricity in CaMnTi2O6. We further explore the material properties of CaMnTi2O6, including its ferroelectric polarization, dielectric and piezoelectric responses, magnetic order, electronic structure, and optical absorption coefficient. It is found that CaMnTi2O6 exhibits room-temperature-stable ferroelectricity and moderate piezoelectric responses. Moreover, CaMnTi2O6 is predicted to have a semiconducting energy band gap similar to that of BiFeO3, and its band gap can further be tuned-via distortions of the planar Mn-O bond lengths. CaMnTi2O6 exemplifies a new class of single-phase semiconducting ferroelectric perovskites for potential applications in ferroelectric photovoltaic solar cells.