Homogenization is a fundamental tool for studying multiscale physical phenomena.A novel numerical homogenization framework called PreFine-Homo is proposed, consisting of pretraining and fine-tuning phases.PreFine-Homo delivers homogenization results up to 1000 times faster than conventional methods in the pretraining phase.The fine-tuning phase of PreFine-Homo enables continuous learning, improvement, and strong extrapolation ability for multiscale homogenization tasks.