As a major component of the LAMOST Galactic surveys, the LAMOST Spectroscopic Survey of the Galactic Anticentre (LSS-GAC) aims to survey a significant volume of the Galactic thin/thick discs and halo for a contiguous sky area of over 3400 deg2 centred on the Galactic anticentre (|b| ≤ 30°, 150 ≤ l ≤ 210°), and obtain λλ3700–9000 low-resolution (R ∼ 1800) spectra for a statistically complete sample of ∼3 M stars of all colours down to a limiting magnitude of r ∼ 17.8 mag (to 18.5 mag for limited fields). Together with Gaia, the LSS-GAC will yield a unique data set to advance our understanding of the structure and assemblage history of the Galaxy, in particular its disc(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 (r ≤ 14 mag) in the Northern hemisphere. During the Pilot and the first year Regular Surveys of LAMOST, a total of 1042 586 750 867 spectra of a signal-to-noise ratio S/N(7450 Å) ≥ 10 S/N(4650 Å) ≥ 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.