Supersonic magneto-hydrodynamic (MHD) turbulence in molecular clouds (MCs) plays an important role in the process of star formation. The effect of the turbulence on the cloud fragmentation process depends on the magnetic field strength. In this work we discuss the idea that the turbulence is super-Alfvénic, at least with respect to the cloud mean magnetic field. We argue that MCs are likely to be born super-Alfvénic. We then support this scenario based on a recent simulation of the large-scale warm interstellar medium turbulence. Using small-scale isothermal MHD turbulence simulation, we also show that MCs may remain super-Alfvénic even with respect to their rms magnetic field strength, amplified by the turbulence. Finally, we briefly discuss the comparison with the observations, suggesting that super-Alfvénic turbulence successfully reproduces the Zeeman measurements of the magnetic field strength in dense MC clouds.