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 ($|b| leq 30^{circ}$, $150 leq l leq 210^{circ}$), and obtain $lambdalambda$3700 -- 9000 low resolution ($R sim 1,800$) spectra for a statistically complete sample of $sim 3$,M stars of all colours down to a limiting magnitued of $r$ $sim$ 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; $r le 14$ 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(7450AA) $ge$ 10 [S/N(4650AA) $ge$ 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.
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