The short-lag spatial coherence (SLSC) imaging has been demonstrated to be advantageous over the traditional B-mode ultrasound imaging. With focused scanning beams, the SLSC imaging has an excellent performance in clutter reduction and lesion detection, especially in the low signal-to-noise ratio (SNR) scenarios. The synthetic aperture (SA) imaging is an appropriate mode for the SLSC imaging as the dynamic transmit focusing could keep a good focusing quality at any depth. However, the SLSC image may still suffer a bad resolution performance when a low lag value is used in the coherence summation to ensure the contrast enhancement. In this paper, an adaptive synthetic transmit (Tx) aperture focusing strategy is proposed for the SLSC imaging with the SA mode. Based on the achievements of adaptive beamforming, a minimum variance beamformer is applied in the Tx aperture to realize adaptive focusing. Spatial coherence is then measured in the receive aperture to form the SLSC image. Simulation and experimental studies were conducted to evaluate the proposed method. Experiments showed that the proposed method not only improved the poor resolution of the original SLSC image but also enhanced the speckle performance, which led to increased contrast-to-noise ratio and speckle SNR values.