The traditional spectral analysis methods of processing spinning satellites laser ranging data have the disadvantages of large computational cost and long processing time. A new satellites laser ranging (SLR) data processing algorithm based on fast Lomb-Scargle algorithm is proposed to solve these problems. Firstly, empirical mode decomposition method is used to adaptively remove the low frequency trend term in the O-C residuals of SLR data, which represents the satellite orbital motion. The preprocessed SLR data is then processed for spectral analysis with fast Lomb-Scargle algorithm to get its periodogram and thus analyze the spinning rate of satellites. Processing the kilohertz SLR data of satellite Ajisai from Graz station of Austria, we can get that the spinning rate of satellite Ajisai during May 2010 is about 0.472 Hz. Further data processing of four passes also have been done by proposed fast algorithm. Results show that the computational cost of spectral analysis is reduced by roughly two orders of magnitude and the processing time is greatly saved by using the fast algorithm. It provides a new way to process large amount of SLR data of spinning satellite fast and efficiently.