  We present our deep $Y$-band imaging data of a two square degree field within
the F22 region of the VIMOS VLT Deep Survey. The observations were conducted
using the WIRCam instrument mounted at the Canada--France--Hawaii Telescope
(CFHT). The total on-sky time was 9 hours, distributed uniformly over 18 tiles.
The scientific goals of the project are to select faint quasar candidates at
redshift $z>2.2$, and constrain the photometric redshifts for quasars and
galaxies. In this paper, we present the observation and the image reduction, as
well as the photometric redshifts that we derived by combining our $Y$-band
data with the CFHTLenS $u^*g'r'i'z'$ optical data and UKIDSS DXS $JHK$
near-infrared data. With $J$-band image as reference total $\sim$80,000
galaxies are detected in the final mosaic down to $Y$-band $5\sigma$ point
source limiting depth of 22.86 mag. Compared with the $\sim$3500 spectroscopic
redshifts, our photometric redshifts for galaxies with $z<1.5$ and
$i'\lesssim24.0$ mag have a small systematic offset of
$|\Delta{z}|\lesssim0.2$, 1$\sigma$ scatter $0.03<\sigma_{\Delta z} < 0.06$,
and less than 4.0% of catastrophic failures. We also compare to the CFHTLenS
photometric redshifts, and find that ours are more reliable at $z\gtrsim0.6$
because of the inclusion of the near-infrared bands. In particular, including
the $Y$-band data can improve the accuracy at $z\sim 1.0-2.0$ because the
location of the 4000\AA-break is better constrained. The $Y$-band images, the
multi-band photometry catalog and the photometric redshifts are released at
\url{http://astro.pku.edu.cn/astro/data/DYI.html}.
