Streaming fair submodular maximization is attracting considerable research interest due to its broad applications in machine learning, particularly for tasks such as feature selection and text summary against large-scale data and fairness considerations. Given a sequence of data points belonging to distinct groups and arriving in a streaming manner, the problem aims to select k data points from the stream to maximize the total revenue of the selected points. In this paper, we first devise an efficient \((\frac{1}{2}-\varepsilon )\) -approximation algorithm with \(O(\log (\frac{1}{\varepsilon }\log \frac{k}{\varepsilon }))\) passes, an improvement over the previous \(O(\frac{1}{\varepsilon }\log \frac{k}{\varepsilon })\) passes. Then, we present a \(\left( \frac{1}{3} - \varepsilon \right) \) -approximation algorithm that needs only one pass and consumes a buffer of size \(O(k+|B|)\) and achieves a ratio strictly greater than \(\frac{1}{4}\) while using a buffer of size \(O(k\log k)\) . Lastly, we conduct extensive experiments using real-world datasets to validate our method, demonstrating that it outperforms all state-of-the-art algorithms in terms of efficiency, effectiveness, and scalability.