We have studied the magnetodielectric response of Y2Cu2O5, the so-called blue phase in the Y2O3-CuO-BaO phase diagram. Based on symmetry principles, we predict and demonstrate magneto-dielectric coupling on a single crystal sample. We report an anomaly in the dielectric constant at the ordering temperature of the Cu spins. We probe the magnetic field-induced phase transitions between four different magnetic phases using magneto-capacitance measurements, demonstrating relatively strong magnetodielectric coupling. We observe an increase in dielectric constant in the spin-flip phase where there exists spontaneous magnetization. We construct a detailed magnetic phase diagram. The magnetodielectric coupling is analyzed in terms of striction induced by symmetric superexchange and optical phonon frequency shifts.