The Hubble constant can be measured from the time delay between pairs of components of a multiply-imaged quasar, depending only on the mass model and the distances to the lens and background source. For a well-determined lens model, H_0 is implicitly related to the observable parameters by H_0 propto sigma_nu^2 Delta tau^{-1}, where sigma_nu is a characteristic velocity dispersion. We present CCD observations of the gravitational lens system Q0957+561A,B in several bands during a period of almost 3 years and new spectroscopic observations of the lens galaxy, G1. A new refined self-consistent test suggests a time delay of 424 days, slightly different from previous estimations. Moreover, the measured velocity dispersion of G1, sigma_l = 310 +- 20 km s^{-1}, is only marginally compatible with the averaged value derived by other authors. With these results, we analize the present models of Q0957+561 and their consequences on H_0.