Adapting pretrained models to downstream tasks is important in practical applications. Existing frameworks adapt from an initial pretrained model to each downstream task directly, but ignore the sequential nature of the downstream tasks and their feedback effect on the pretrained model. In this work, we propose a new framework, called BiKT, to enable bidirectional knowledge transfer between pretrained models and downstream tasks in rounds. We model each downstream task in the current round as a target task for adaptation and treat all the tasks in the previous rounds as source tasks for feedback. We design a feedback algorithm by multi-task learning over the labeled data of the source tasks, where task-specific prompts are plugged into the backbone network for decoupling task-exclusive knowledge from task-shared knowledge. We further utilize the good initiation of the new backbone network updated in the feedback phase and the trained prompts of the source tasks for adaptation. Evaluation over 9 GLUE datasets, 6 SuperGLUE datasets, and 8 other datasets using models with different pretraining levels and different parameter scales shows remarkable improvement in full-shot and few-shot adaptation settings.