We present the result of a search for very metal-poor (VMP, [Fe/H]{<}-2.0) stars in the Milky Way based on low-resolution spectra from Large sky Area Multi-Object fiber Spectroscopic Telescope (LAMOST) DR3, significantly enlarging the current candidate sample of these low-metallicity objects. The selection procedure results in a sample of 10008 VMP stars covering a large area of sky in the Northern Hemisphere, and includes over 6800 targets brighter than V~16. This LAMOST DR3 VMP sample provides the largest number of VMP candidates to date that are sufficiently bright for follow-up high-resolution observation with 4-10m telescopes, greatly expanding the VMP stars discovered in the northern sky, and can be used to balance the spatial distribution of VMP stars with high-resolution spectroscopic analyses. Comparison with stars having existing high-resolution analyses and Tycho Gaia Astrometric Solution parallaxes indicates that the derived stellar parameters and distance estimates are reliable. The sample reaches beyond 40kpc in the halo, and contains over 670 candidates of extremely metal-poor ([Fe/H]{<}-3.0) and ultra-metal-poor ([Fe/H]{<}-4.0) stars. The distribution of V{phi} indicates that the sample consists of two halo components, with the retrograde component likely to be associated with the outer-halo population. A new criterion is proposed to select carbon-enhanced metal-poor (CEMP) star candidates, using line indices G1 and EGP over the range 4000K<Teff<7000K, resulting in 636 CEMP candidates from the LAMOST DR3 VMP sample.