Meteorological observation data have observational errors inevitably. It is an ill-posed inverse problem to perform the derivation of discrete data with observation errors. In order to solve the perplexing problem, this paper puts forward the new algorithm which reconstructs the first-order partial derivatives of the two-dimensional observation data in the rectangular region， which is based on the idea of Tikhonov regularization . We test the performance of the algorithm with a series of simulating observation data, the results show that the algorithm is effective and has higher accuracy. It is feasible to analyze meteorological observation data with the algorithm and can enhance the recognizing ability for the small-scale weather systems.