For high-speed train (HST) millimeter wave (mmWave) communications, the use of narrow beams with small beam coverage needs frequent beam switching, while wider beams with small beam gain leads to weaker mmWave signal strength. In this paper, we consider beam switching based beam design, which is formulated as an optimization problem aiming to minimize the number of switched beams within a predetermined railway range subject to that the receiving signal-to-noise ratio (RSNR) at the HST is no lower than a predetermined threshold. To solve this problem, we propose two sequential beam design schemes, both including two alternately-performed stages. In the first stage, given an updated beam coverage according to the railway range, we transform the problem into a feasibility problem and further convert it into a min-max optimization problem by relaxing the RSNR constraints into a penalty of the objective function. In the second stage, we evaluate the feasibility of the beamformer obtained from solving the min-max problem and determine the beam coverage accordingly. Simulation results show that compared to the first scheme, the second scheme can achieve 96.20\% reduction in computational complexity at the cost of only 0.0657\% performance degradation.