Crawling Wave Sonoelastography is quantitative ultrasound-based elastography approach that provides tissue stiffness information. Two mechanical sources generates an interference pattern on a tissue with obtaining a shear wave speed (SWS) map. To do this task, many estimators have been developed; however, one of the most common non solved issues is the present of artifacts on the SWS map reconstruction. In this study, a new SWS estimator based on the Short-Time Fourier Transform is proposed. Testing is made with data acquired from experiments on a gelatin phantom with a circular inclusion vibrating on a range between 200 Hz and 360 Hz with steps of 20 Hz. The results were compared with the Phase Derivative estimator. The proposed estimator generated a SWS image with lower coefficient of variation and higher Contrast-to-Noise Ratio, which may allow better discrimination between regions.