Various approaches have been proposed to release histogram on static datasets with differential privacy, while little work exist that handle dynamic datasets. Those existing static approaches are ill-suited for the practical applications on data stream due to the inherent complexity of publishing streaming histograms. With this consideration, this paper addresses the challenge by proposing a partitioning-based method, called SHP (streaming histogram publication), which partitions the count values of each sliding window into different groups for releasing the final histogram. In view of different global sensitivity of queries adopted by this paper, three incremental utility-based mechanisms for adding Laplace noise are proposed to achieve differential privacy. The three mechanisms are sliding window mechanism, time point mechanism, and adaptive sampling mechanism, respectively. In the third mechanism, SHP relies on the adaptive sampling method to predict the next arriving count value at non-sampling time points. If the difference between the predicted value and the true value is less than a user-defined threshold, then it releases the predicted value, otherwise, releases the true value. This mechanism can save privacy budget in terms of sampling interval updates. Experimental results or real datasets show that the utility of SHP based on sampling is better than the other two mechanisms.