In the Southeast Margin of the Tibetan Plateau, low-velocity sedimentary layers that would significantly affect the accuracy of the H-κ stacking of receiver functions are widely distributed. In this study, we use teleseismic waveform data of 475 events from 97 temporary broadband seismometers deployed by ChinArray Phase I to obtain crustal thicknesses and Poisson’s ratios within the Chuxiong-Simao Basin and adjacent area, employing an improved method in which the receiver functions are processed through a resonance-removal filter, and the H-κ stacking is time-corrected. Results show that the crustal thickness ranges from 30 to 55 km in the study area, reaching its thickest value in the northwest and thinning toward southwest, southeast and northeast. The apparent variation of crustal thickness around the Red River Fault supports the view of southeaste escape of the Tibetan Plateau. Relatively thin crustal thickness in the zone between Chuxiong City and the Red River Fault indicates possible uplift of mantle in this area. The positive correlation between crustal thickness and Poisson’s ratio is likely to be related to lower crust thickening. Comparison of results obtained from different methods shows that the improved method used in our study can effectively remove the reverberation effect of sedimentary layers.