The effects of random bends on the baseband frequency response of the multimode optical fiber are very important in practical communication systems. But their theoretical investigation has not been fully carried out. Therefore in this paper we theoretically investigate the baseband frequency characteristics of the multimode fiber whose axis suffers from random bends with the help of the variational method. As a result, we obtain the phase characteristics as well as the amplitude characteristics and indicate that the phase distortion can be neglected within the bandwidth. Also, we confirm the existence of the quasi-steady state, in which the transmission characteristics are fairly stabilized, although the bandwidth is not always proportional to the inverse square root of the fiber length.