We develop a new diagnostic method to classify galaxies into active galactic nucleus (AGN) hosts, star-forming galaxies, and absorption-dominated galaxies by combining the [OIII]/H{beta} ratio with rest-frame U-B color. This can be used to robustly select AGNs in galaxy samples at intermediate redshifts (z<1). We compare the result of this optical AGN selection with X-ray selection using a sample of 3150 galaxies with 0.3<z<0.8 and I_AB_<22, selected from the DEEP2 Galaxy Redshift Survey and the All-wavelength Extended Groth Strip International Survey. Among the 146 X-ray sources in this sample, 58% are classified optically as emission-line AGNs, the rest as star-forming galaxies or absorption-dominated galaxies. The latter are also known as "X-ray bright, optically normal galaxies" (XBONGs).