We have studied the statistical properties of turbulence in molecular clouds identified in the Boston University - Five College Radio Astronomy Observatory (BU-FCRAO) Galactic Ring Survey (GRS). Toward this end, the probability density function (PDF) and velocity distribution were measured for about 50 molecular clouds. We found there exists a good correlation between the PDF width and the velocity dispersion for these molecular clouds. In order to investigate how general properties of astrophysical turbulence depends on the plasma parameters such as magnetic field strength and sonic Mach number, we performed three-dimensional MHD simulations. We then examined if the observed characteristics of interstellar turbulence are consistent with theoretical results from MHD simulations.