Context. Massive binary stars play a crucial role in many astrophysical fields. Investigating the statistical properties of massive binary stars is essential to trace the formation of massive stars and constrain the evolution of stellar populations. However, no consensus has been achieved on the statistical properties of massive binary stars, mainly due to the lack of a large and homogeneous sample of spectroscopic observations. Aims. We study the intrinsic binary fraction f(b)(in) and distributions of mass ratio f(q) and orbital period f(P) of early-type stars (comprised of O-, B-, and A-type stars) and investigate their dependences on effective temperature T-eff, stellar metallicity [M/H], and the projection velocity v sin i, based on the homogeneous spectroscopic sample from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) Data Release Eight (DR8). Methods. We collected 886 early-type stars, each with more than six observations from the LAMOST DR8, and divided the sample into subgroups based on their derived effective temperature (T-eff), metallicity ([M/H]), and projected rotational velocity (v sin i). Radial velocity measurements were archived from a prior study. A set of Monte Carlo simulations, following distributions of f(P) proportional to P-pi and f (q) proportional to q(gamma) were applied to the observed binary fraction to correct for any observational biases. The uncertainties of the derived results induced by the sample size and observation frequency are examined systematically. Results. We found that f(b)(in) increases with increasing T-eff . For stars in groups of B8-A, B4-B7, O-B3, the binary fractions are f(b)(in) = 48% +/- 10%, 60% +/- 10%, and 76% +/- 10%, respectively. The binary fraction is positively correlated with metallicity for spectra in the sample, with derived values of f(b)(in) = 44% +/- 10%, 60% +/- 10%, and 72% +/- 10% for spectra with metallicity ranges of [M/H] < -0.55, - 0.55 <= [M/H] < -0.1, to [M/H] >= -0.1. Over all the v sin i values we considered, the f(b)(in) have constant values of similar to 50%. It seems that the binary population is relatively evenly distributed over a wide range of v sin i values, while the whole sample shows that most of the stars are concentrated at low values of v sin i (probably from strong wind and magnetic braking of single massive stars) and at high values of v sin i (likely from the merging of binary stars). Stellar evolution and binary interaction may be partly responsible for this. In the case of samples with more than six observations, we derived pi = -0.9 +/- 0.35, -0.9 +/- 0.35, and -0.9 +/- 0.35, and gamma = -1.9 +/- 0.9, - 1.1 +/- 0.9, and -2 +/- 0.9 for stars of types O-B3, B4-B7, and B8-A, respectively. There are no correlations found between pi(gamma) and T-eff, nor for pi(gamma) and [M/H]. The uncertainties of the distribution decrease toward a larger sample size with higher observational cadence.