We report the discovery of 28 candidate high-velocity stars (HVSs) at heliocentric distances of less than 3 kpc, based on the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) Data Release 1. All candidates have velocities, with respect to the Galactic rest frame, in excess of 300 km s−1; 12 objects move faster than 400 km s−1. Our sample of HVS candidates covers a much broader color range than the equivalent ranges discussed in previous studies and comprises the first and largest sample of HVSs in the solar neighborhood. The observed as well as the derived parameters for all candidates are sufficiently accurate to allow us to ascertain their nature as genuine HVSs, of which a subset of 12 objects represents the most promising candidates. Our results also highlight the great potential of discovering statistically large numbers of HVSs of different spectral types in LAMOST survey data. The results reported here also highlight the great potential of discovering statistically large numbers of HVSs of different spectral types in LAMOST survey data. We will continue to perform further systematic HVS searches based on the LAMOST data; the resulting stellar samples will eventually enable us to better understand the nature of the HVSs themselves and ultimately constrain the structure of the Galaxy. As a consequence, it is of great importance for investigating the various HVS ejection mechanisms, which may be more complex than previously thought.