A method is proposed to estimate the mass centre position and tumbling motion of rocket body using diffuse reflection laser ranging data. The tumbling motion of rocket body is analysed and the diffuse reflection laser ranging model is built. The theoretical and simulation methods are presented to estimate the tumbling axis orientation and tumbling period of rocket body. The laser ranging data of last stage Soyuz rocket body measured at Wettzell station are processed with the fast Lomb-Scargle algorithm. The length and mass centre position of rocket body are deduced by comparing the histograms of simulated and measured data. The tumbling period is estimated to be 11.4 s, the right ascension is 203°, and the declination is 23°.