Dielectric constants and Raman spectra of single crystal CuO were measured at temperatures between 77 and 295 K. Through dielectric measurements, we observed dielectric anomalies at the two successive magnetic transitions 230 K and 213 K along the three crystal axes, which is in consistence with our previously reported dielectric-magnetic coupling. Beside the well-known low-temperature band in Raman spectra, which originates from a strong magnon-phonon coupling effect, the temperature dependences of the Raman shift, intensity and linewidth of the Raman modes have revealed anomalous behaviors near the magnetic transitions. The present features are considered to be correlated with the multiferroic transition in this multiferroic material.