This paper focuses on sea surface wind speed estimation based on cyclone global navigation satellite system reflectometry (GNSS-R) data. In order to extract useful information from delay-Doppler map (DDM) data, three delay waveforms are presented for wind speed estimation. The delay waveform without Doppler shift is defined as central delay waveform (CDW), and the integral of the delay waveforms with different Doppler shift values is defined as integral delay waveform (IDW), while the difference between normalized IDW (NIDW) and normalized CDW (NCDW) is defined as differential delay waveform (DDW). We first propose a data filtering method based on threshold setting for data quality control. This method can select good-quality DDM data by adjusting the root mean square (RMS) threshold of cleaned DDW. Then, the normalized bistatic radar scattering cross section (NBRCS) and the leading edge slope (LES) of IDW are calculated using clean DDM data. Wind speed estimation models based on NBRCS and LES observations are then developed, respectively, and on this basis, a combination wind speed estimation model based on determination coefficient is further proposed. The CYGNSS data and ECMWF reanalysis data collected from 12 May 2020 to 12 August 2020 are used, excluding data collected on land, to evaluate the proposed models. The evaluation results show that the wind speed estimation accuracy of the piecewise function model based on NBRCS is 2.3 m/s in terms of root mean square error (RMSE), while that of the double-parameter and triple-parameter models is 2.6 and 2.7 m/s, respectively. The wind speed estimation accuracy of the double-parameter and triple-parameter models based on LES is 3.3 and 2.5 m/s. The results also demonstrate that the RMSE of the combination method is 2.1 m/s, and the coefficient of determination is 0.906, achieving a considerable performance gain compared with the individual NBRCS- and LES-based methods.