In this study, the temperature effects on moisture diffusion of epoxy resin and its glass/carbon fibre-reinforced epoxy composites in distilled water were tested. In 70 degrees C, their diffusion coefficients were found 20.9 times, 16.5 times and 29.5 times higher than those in room temperature (25 degrees C); meanwhile, their saturated moisture contents were measured increased by 1.68 times, 2.39 times and 2.55 times, respectively. Furthermore, a cyclic moisture absorption-desorption experiment of composite materials was designed and implemented. The results revealed that moisture weight gain is no longer well described by Fick's law during the second and the third cycle of moisture absorption processes, e.g., moisture diffusion coefficients in these two periods are obviously higher and lower than the predictions by Fick's law during the first half and second half of moisture absorption processes. A flux-dependent moisture diffusion model proposed represents this phenomenon. In this model, moisture diffusion coefficient is formulated exponentially depending upon water flux. Flexural strength degenerations of the bulk epoxy and composite materials were tested corresponding to saturated state and re-dried state of per cycle, after three moisture absorption-desorption cycles, the dry state strength retention rates of bulk epoxy, UD-GFRP and UD-CFRP are 93, 79 and 80%, and in wet state these rates decrease to 53, 48 and 78%, respectively.