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As research interest surges, vector similarity search is applied in multiple fields, including data mining, computer vision, and information retrieval. {Given a set of objects (e.g., a set of images) and a query object, we can easily transform each object into a feature vector and apply the vector similarity search to retrieve the most similar objects. However, the original vector similarity search cannot well support \textit{hybrid queries}, where users not only input unstructured query constraint (i.e., the feature vector of query object) but also structured query constraint (i.e., the desired attributes of interest). Hybrid query processing aims at identifying these objects with similar feature vectors to query object and satisfying the given attribute constraints. Recent efforts have attempted to answer a hybrid query by performing attribute filtering and vector similarity search separately and then merging the results later, which limits efficiency and accuracy because they are not purpose-built for hybrid queries.} In this paper, we propose a native hybrid query (NHQ) framework based on proximity graph (PG), which provides the specialized \textit{composite index and joint pruning} modules for hybrid queries. We easily deploy existing various PGs on this framework to process hybrid queries efficiently. Moreover, we present two novel navigable PGs (NPGs) with optimized edge selection and routing strategies, which obtain better overall performance than existing PGs. After that, we deploy the proposed NPGs in NHQ to form two hybrid query methods, which significantly outperform the state-of-the-art competitors on all experimental datasets (10$\times$ faster under the same \textit{Recall}), including eight public and one in-house real-world datasets. Our code and datasets have been released at \url{https://github.com/AshenOn3/NHQ}.