Dynamic binaural rendering of Ambisonics considering head movements gives a highly realistic sensation to listeners owing to the precise localization and the presence of dynamic cues. Dealing with a head movement is often achieved in the spherical harmonic domain by multiplying Ambisonic signals by a Wigner D-matrix (WDM) with the aim of rotating signals in the opposite direction to the head movement. However, for a vertical rotation, the system requires an enormous computational cost owing to the structure of the WDM, whose number of block diagonal elements increases with the spherical harmonic order of Ambisonics. In this paper, a method is introduced to reduce the computational cost related to the vertical rotation by approximating a WDM with a banded WDM generated from the truncated sum of a power series expression of the WDM. By using an analytically derived upper bound of the approximation error, two methods are devised to determine the minimum bandwidth which archives the maximum computational cost reduction under the user-preferred threshold. The experimental results show that there is a trade-off between the approximation error and the computational cost and that these methods are applicable to the use case of interest, i.e., dynamic binaural rendering of Ambisonics.