In this paper we present our results of a comprehensive spectroscopic analysis of WASP-1 , the host star to the exoplanet WASP-1b . We derive T _ { eff } = 6110 \pm 45 K , \log g = 4.28 \pm 0.15 , and [ M/H ] = 0.23 \pm 0.08 , and also a high abundance of lithium , \log n ( { Li } ) = 2.91 \pm 0.05 . These parameters suggests an age for the system of 1–3 Gyr and a stellar mass of 1.25–1.35 M _ { \odot } . This means that WASP-1 has properties very similar to those of HD 149026 , the host star for the highest density planet yet detected . Moreover , their planets orbit at comparable distances and receive comparable irradiating fluxes from their host stars . However , despite the similarity of WASP-1 with HD 149026 , their planets have strongly different densities . This suggests that gas-giant planet density is not a simple function of host-star metallicity or of radiation environment at ages of \sim 2 Gyr .