We present the results of axisymmetric time-dependent hydrodynamic calculations of line-driven winds from accretion disks in active galactic nuclei (AGN). We assume the disk is flat, Keplerian, geometrically thin, and optically thick, radiating according to the α-disk prescription. The central engine of the AGN is a source of both ionizing X-rays and wind-driving ultraviolet (UV) photons. To calculate the radiation force, we take into account radiation from the disk and the central engine. The gas temperature and ionization state in the wind are calculated self-consistently from the photoionization and heating rate of the central engine. We find that a disk accreting onto a 10 8 M ⊙ yr −1 black hole at the rate of 1.8 M ⊙ yr −1 can launch a wind at ∼ 10 16 cm from the central engine. The X-rays from the central object are significantly attenuated by the disk atmosphere so they cannot prevent the local disk radiation from pushing matter away from the disk. However in the supersonic portion of the flow high above the disk, the X-rays can overionize the gas and decrease the wind terminal velocity. For a reasonable X-ray opacity, e.g., κ X = 40 g −1 cm 2, the disk wind can be accelerated by the central UV radiation to velocities of up to 15000 km s −1 at a distance of ∼ 10 17 cm from the central engine. The covering factor of the disk wind is ∼ 0.2. The wind is unsteady and consists of an opaque, slow vertical flow near the disk that is bounded on the polar side by a high-velocity, stream. A typical column density through the fast stream is a few 10 23 cm −2 so the stream is optically thin to the UV radiation. This low column density is precisely why gas can be accelerated to high velocities. The fast stream contributes nearly 100% to the total wind mass loss rate of 0.5 M ⊙ yr −1.