Current research on statistical publication of differential privacy data stream only considers one-dimensional data stream. However, many applications require privacy protection publishing two-dimensional data stream, which makes traditional models and methods unusable. To solve the issue, firstly, a differential privacy statistical publication algorithm for fixed-length two-dimensional data stream, call PTDSS, was proposed. The tuple frequency of the two-dimensional data stream under certain condition was calculated by a one-time linear scan to the data stream with low-cost space. Basing on the result of sensitivity analysis, a certain amount of noise was added into the statistical results so as to meet the differential privacy requirement. After that, a differential privacy continuous statistical publication algorithm for any length two-dimensional data stream using sliding window model, called PTDSS-SW, was presented. The theoretical analysis and experimental results show that the proposed algorithms can safely preserve the privacy in the statistical publication of two-dimensional data stream and ensure the relative error of the released data in the range of 10% to 95%.