Beam hopping technology is considered to provide a high level of flexible resource allocation to manage uneven traffic requests in multi-beam high throughput satellite systems. Conventional beam hopping resource allocation methods assume constant rainfall attenuation. Different from conventional methods, by employing genetic algorithm this paper studies dynamic beam hopping time slots allocation under the effect of time-varying rain attenuation. Firstly, a beam hopping system model as well as rain attenuation time series based on Dirac lognormal distribution are provided. On this basis, the dynamic allocation method by employing genetic algorithm is proposed to obtain both quantity and arrangement of time slots allocated for each beam. Simulation results show that, compared with conventional methods, the proposed algorithm can dynamically adjust time slots allocation to meet the non-uniform traffic requirements of each beam under the effect of time-varying rain attenuation and effectively improve system performance.