We investigate the cosmological observational test of extended quintessence model, i.e. a scalar-tensor gravity model with scalar field potential serving as dark energy, by using Planck 2018 cosmic microwave background (CMB) data, together baryon acoustic oscillations (BAO) and redshift-space distortion (RSD) data. As an example, we consider Brans-Dicke kinetic term $\frac{\omega(\phi)}{\phi} \...