In recent years, graph prompt learning/tuning has garnered increasing attention in adapting pre-trained models for graph representation learning. As a kind of universal graph prompt learning method, Graph Prompt Feature (GPF) has achieved remarkable success in adapting pre-trained models for Graph Neural Networks (GNNs). By fixing the parameters of a pre-trained GNN model, the aim of GPF is to modify the input graph data by adding some (learnable) prompt vectors into graph node features to better align with the downstream tasks on the smaller dataset. However, existing GPFs generally suffer from two main limitations. First, GPFs generally focus on node prompt learning which ignore the prompting for graph edges. Second, existing GPFs generally conduct the prompt learning on all nodes equally which fails to capture the importances of different nodes and may perform sensitively w.r.t noisy nodes in aligning with the downstream tasks. To address these issues, in this paper, we propose a new unified Graph Selective Prompt Feature learning (GSPF) for GNN fine-tuning. The proposed GSPF integrates the prompt learning on both graph node and edge together, which thus provides a unified prompt model for the graph data. Moreover, it conducts prompt learning selectively on nodes and edges by concentrating on the important nodes and edges for prompting which thus make our model be more reliable and compact. Experimental results on many benchmark datasets demonstrate the effectiveness and advantages of the proposed GSPF method.