Few-Shot Molecular Property Prediction (FSMPP) is an improtant task on drug discovery, which aims to learn transferable knowledge from base property prediction tasks with sufficient data for predicting novel properties with few labeled molecules. Its key challenge is how to alleviate the data scarcity issue of novel properties. Pretrained Graph Neural Network (GNN) based FSMPP methods effectively address the challenge by pre-training a GNN from large-scale self-supervised tasks and then finetuning it on base property prediction tasks to perform novel property prediction. However, in this paper, we find that the GNN finetuning step is not always effective, which even degrades the performance of pretrained GNN on some novel properties. This is because these molecule-property relationships among molecules change across different properties, which results in the finetuned GNN overfits to base properties and harms the transferability performance of pretrained GNN on novel properties. To address this issue, in this paper, we propose a novel Adaptive Transfer framework of GNN for FSMPP, called ATGNN, which transfers the knowledge of pretrained and finetuned GNNs in a task-adaptive manner to adapt novel properties. Specifically, we first regard the pretrained and finetuned GNNs as model priors of target-property GNN. Then, a task-adaptive weight prediction network is designed to leverage these priors to predict target GNN weights for novel properties. Finally, we combine our ATGNN framework with existing FSMPP methods for FSMPP. Extensive experiments on four real-world datasets, i.e., Tox21, SIDER, MUV, and ToxCast, show the effectiveness of our ATGNN framework.