In the wireless communication systems, the bandwidth is usually variable because of the dynamic channel. Although the optimal number of subpackets and AMC scheme has been proposed recently, it is limited to the fixed bandwidth. In this paper, a cross-layer design named AMC-SPS-SVB which combines AMC and ASPS with SR-ARQ is proposed to maximize the throughput of the system in a dynamic channel with the variable bandwidth. Curve fitting is applied here to give out approximate expressions of bit error rate under given modulation and coding schemes. General closed-form expressions of effective spectrum efficiency and optimal subpackt size under given modulation and coding schemes for our algorithm are presented. Furthermore, an efficient method is provided to find the optimal AMC and subpacket size. Numerical results show that the proposed algorithm improves the throughput of the system and works well with the variable bandwidth.