Abstract: The new vacuum solar telescope at the Fuxian Lake Solar Observation Station is currently the largest ground-based solar telescope in China. It can simultaneously collect Tio and Hα solar images. In this paper we present a method of processing Hα solar chromosphere images observed with the new telescope by selecting image frames of sufficient quality. The method is mainly based on the frame-selection technique and the Shift-And-Add (SAA) technique. It is for online publishing of observational data from the new telescope. The frame-selection technique incorporates the Speckle Interferometry (SI) and is originally used for observation of the solar photosphere. This technique can cleanly subtract object intensities in images to retain only distortions due to the telescope and atmospheric turbulences. For extended objects such as the sun, the shift vector in an SAA operation is usually determined by cross correlating observed-data frames with a reference frame, which is the best-quality frame among the data frames. Our method is simple and fast, e.g., it can reconstruct data in much less time than the speckle-masking method. Results from this method can also be processed with other methods (e.g. the speckle-masking method) if needed. We briefly describe the SAA and SI techniques, including some results of the SI technique. We finally present processing results of some observational data using our method.