We theoretically study the role of dispersion in propagation of rotating beams in left-handed materials (LHMs). By modeling the rotating beam as a superposition of two rotating Laguerre-Gaussian beams with opposite chirality, same magnitude and different frequencies, we demonstrate that the rotation property of the rotating beam in LHM is significantly dependent on the sign and strength of dispersion: In the normal dispersion region, the direction of transverse energy flow is reversed compared to the vacuum, due to the negative refractive index of LHM, while in the anomalous dispersion region it may be parallel or antiparallel to that in the case of vacuum, depending on the strength of dispersion. In addition, we find that the angular momentum density can be parallel or antiparallel to the transverse energy flow in LHM, while the angular momentum flow is always opposite to the transverse energy flow.