I estimate the size and shape of the near-Earth asteroid (NEA) population using survey data from the Lincoln Near-Earth Asteroid Research (LINEAR) project, covering 375,000 square degrees of sky and including more than 1300 NEA detections. A simulation of detection probabilities for different values of orbital parameters and sizes combined with the detection statistics in a Bayesian framework provides a correction for observational bias and yields the NEA population distribution as a function of absolute magnitude, semi-major axis, eccentricity, and inclination. The NEA population is more highly inclined than previously estimated, and the total number of kilometer-sized NEAs is 1227(-90)(+170) (1sigma).