As a major component of the LAMOST Galactic surveys, the LAMOST Spectroscopic Survey of the Galactic Anti-centre (LSS-GAC) aims to survey a significant volume of the Galactic thin/thick discs and halo for a contiguous sky area of over 3,400 deg 2 centred on the Galactic anti-centre (|b| 30• , 150 l 210 • ), and obtain λλ3700 -9000 low resolution (R ∼ 1, 800) spectra for a statistically complete sample of ∼ 3 M stars of all colours down to a limiting magnitued of r ∼ 17.8 mag (to 18.5 mag for limited fields). Together with Gaia, the LSS-GAC will yield a unique dataset to advance our understanding of the structure and assemblage history of the Galaxy, in particular its disk(s). In addition to the main survey, the LSS-GAC will also target hundreds of thousands objects in the vicinity fields of M 31 and M 33 and survey a significant fraction (over a million) of randomly selected very bright stars (VB; r 14 mag) in the northern hemisphere. During the Pilot and the first year Regular Surveys of LAMOST, a total of 1,042,586 [750,867] spectra of a signal to noise ratio S/N(7450Å) 10 [S/N(4650Å) 10] have been collected. In this paper, we present a detailed description of the target selection algorithm, survey design, observations and the first data release of value-added catalogues (including radial velocities, effective temperatures, surface gravities, metallicities, values of interstellar extinction, distances, proper motions and orbital parameters) of the LSS-GAC.