Nowadays, many practical applications need to publish streaming data continuously. Most of existing research works for differential privacy single streaming data publication focus on range accumulation. However, many practical scenarios need to answer arbitrary range counting queries of streaming data. At the same time, there exist specific rules of queries from users, so adaptive analysis and calculation for historical queries should be concerned. To improve the usability of published data, an algorithm HQ_DPASP for differential privacy streaming data adaptive publication based on historical queries is proposed. Combining the characteristics of streaming data, HQ_DPASP firstly uses the sliding window mechanism to construct the differential privacy range tree of the streaming data dynamically. Secondly, by analyzing the coverage probability of tree nodes and calculating the privacy parameters from leaves to root, HQ_DPASP allocates privacy budget from root to leaves and adds non-uniform noise on tree nodes. Finally, the privacy budget of tree nodes and tree's parameters are adjusted adaptively based on the characteristic of historical queries. Experiments are designed for testing the feasibility and effectiveness of HQ_DPSAP. The results show that HQ_DPSAP is effective in answering arbitrary range counting queries on the published streaming data while assuring low mean squared error of queries and high algorithm efficiency.