  We report the result of a faint quasar survey in a one square degree field.
The aim is to test the Y-K/g-z and J-K/i-Y color selection criteria for quasars
at faint magnitude, to obtain a complete sample of quasars based on deep
optical and near-infrared color-color selection, and to measure the faint end
of quasar luminosity function (QLF) over a wide redshift range. We carried out
a quasar survey based on the Y-K/g-z and J-K/i-Y quasar selection criteria,
using the deep Y-band data obtained from our CFHT/WIRCam Y-band images in a
two-degree field within the F22 field of the VIMOS VLT deep survey, optical
co-added data from Sloan Digital Sky Survey Stripe 82 and deep near-infrared
data from the UKIDSS Deep Extragalactic Survey in the same field. We discovered
25 new quasars at 0.5 < z < 4.5 and i < 22.5 mag within one square degree
field. The survey significantly increases the number of faint quasars in this
field, especially at z ~ 2-3. It confirms that our color selections are highly
complete in a wide redshift range (z < 4.5), especially over the quasar number
density peak at z ~ 2-3, even for faint quasars. Combining all previous known
quasars and new discoveries, we construct a sample with 109 quasars, and
measure the binned QLF and parametric QLF. Although the sample is small, our
results agree with a pure luminosity evolution at lower redshift and luminosity
evolution and density evolution model at redshift z > 2.5.
