We obtain cosmological constraints from a measurement of the spherically averaged power spectrum of the distribution of about 90 000 luminous red galaxies (LRGs) across 7646 deg2 in the Northern Galactic Cap from the seventh data release (DR7) of the Sloan Digital Sky Survey. The errors and mode correlations are estimated thanks to the 160 LasDamas mock catalogues, created in order to simulate the same galaxies and to have the same selection as the data. We apply a model that can accurately describe the full shape of the power spectrum with the use of a small number of free parameters. Using the LRG power spectrum, in combination with the latest measurement of the temperature and polarization anisotropy in the cosmic microwave background (CMB), the luminosity–distance relation from the largest available Type 1a supernovae (SNIa) data set and a precise determination of the local Hubble parameter, we obtain cosmological constraints for five different parameter spaces. When all the four experiments are combined, the flat ΛCDM model is characterized by , Ωb= 0.045 ± 0.001, ns= 0.963 ± 0.011, σ8= 0.802 ± 0.021 and H0= 71.2 ± 1.4 km s−1 Mpc−1. When we consider curvature as a free parameter, we do not detect deviations from flatness: Ωk= (1.6 ± 5.4) × 10−3, when only CMB and the LRG power spectrum are used; the inclusion of the other two experiments does not improve this result substantially. We also test for possible deviations from the cosmological constant paradigm. Considering the dark energy equation of state parameter wDE as time independent, we measure , if the geometry is assumed to be flat, otherwise. When describing wDE through a simple linear function of the scale factor, our results do not evidence any time evolution. In the next few years new experiments will allow us to measure the clustering of galaxies with a precision much higher than achievable today. Models like the one used here will be a valuable tool in order to achieve the full potentials of the observations and obtain unbiased constraints on the cosmological parameters.