There is strong evidence for magnetic fields in molecular clouds to be oriented parallel to the direction of bipolar outflows. We have evidence for Alfvén waves in molecular clouds from the facts that: (i) the velocity width of CO lines, ΔV, is approximately twice the gravitational energy, and (ii) polarization maps indicate well-defined magnetic fields. These facts indicate that ΔV is wave-like and not eddy-like. We study the Alfvén wave protostellar model of Jatenco-Pereira and Opher (1989) to explain the observed bipolar outflows and turbulence in molecular clouds. We assume that the Alfvén waves are primarily dissipated by non-linear damping and examine the physical parameters necessary to produce the observed massive low-velocity bipolar outflows (u∞ ∿ 10 − 50 km s−1 and Ṁ ∿ 10−3 M⊙ yr−1) and turbulence in molecular clouds.