  We study matter density perturbations up to third order and the one-loop
matter power spectrum in degenerate higher-order scalar-tensor (DHOST) theories
beyond Horndeski. We systematically solve gravitational field equations and
fluid equations order by order, and find three novel shape functions
characterizing the third-order solution in DHOST theories. A complete form of
the one-loop matter power spectrum is then obtained using the resultant second-
and third-order solutions. We confirm the previous result that the convergence
condition of the loop integrals in the infrared limit becomes more stringent
than that of the standard one in general relativity. We show that also in the
ultraviolet limit the convergence condition becomes more stringent and the
one-loop matter power spectrum is thus sensitive to the short-wavelength
behavior of the linear power spectrum.
