In this paper, an efficient neural-network-based adaptive DPD design which performs well under power varying conditions is presented. The DPD design is derived on the basis of the envelop timedelay neural network (ETDNN). The redefined ETDNN-DPD requires the part of parameter updates, which enables to adapt it to the rapid change of power amplifier (PA) distortion. Additionally, the redefined ETDNN-DPD also maintains the stability of the compensation performances under varying power condition while its structure is pruned by the structured pruning. Furthermore, to verify its practical use, we also propose the weight scaling technique, which reduces multiplications of the redefined ETDNN-DPD, and applied it to the implementation of the redefined ETDNN-DPD on FPGA. Compared FPGA-implemented ETDNN-DPD with FPGA-implemented conventional memory polynomial DPD, we verified that our proposed DPD achieved 3.2 dB better error vector magnitude (EVM) while lower hardware resource utilization at the fixed power level. Moreover, our proposed DPD kept better performance under the varying power condition only by the partial update of its parameters than memory polynomial DPD.