Horndeski theory is the most general scalar-tensor theory which leads to the second-order equations of motion. In this talk, a subclass of the Horndeski theory with shift symmetry is applied to study the galaxy rotation curve and the cosmo- logical evolution with identifying the scalar field with the dark matter, while the cosmological constant explains the dark energy. I show an analytic solution which reproduces the inverse-square-law density distribution of dark matter halo, so that the observed rotation curve can be explained at the galactic scale. I also discuss the dark-matter-like behavior of the scalar field at the cosmological scale and consider the consistent parameter region between the galactic and cosmological scales.