The anisotropic galaxy clustering on large scales provides us with a unique opportunity to probe into the gravity theory through the redshift-space distortions (RSDs) and theAlcock-Paczynski effect. Using the multipole power spectra up to hexadecapole (ℓ = 4), of the luminous red galaxy (LRG) sample in the Data Release 7 (DR7) of the Sloan Digital Sky Survey II (SDSS-II), we obtain simultaneous constraints on the linear growth rate f, angular diameter distance DA, and Hubble parameter H at redshift z = 0.3. For this purpose, we first extensively examine the validity of a theoretical model for the non-linear RSDs using mock subhalo catalogues from N-body simulations, which are constructed to match with the observed multipole power spectra. We show that the input cosmological parameters of the simulations can be recovered well within the error bars by comparing the multipole power spectra of our theoretical model and those of the mock subhalo catalogues. We also carefully examine systematic uncertainties in our analysis by testing the dependence on prior assumption of the theoretical model and the range of wavenumbers to be used in the fitting. These investigations validate that the theoretical model can be safely applied to the real data. Thus, our results from the SDSS DR7 LRG sample are robust including systematics of theoretical modelling; f(z = 0.3)7σ88(z = 0.3) = 0.49 ± stat. .0.08 ± sys. 0.04, DA(z = 0.3) = 968 ± stat. 42 ± sys. 17 (Mpc), H(z = 0.3) = 81.7 ±stat. 5.0 ± sys. 3.7 (km s-1 Mpc-1). We believe that our method to constrain the cosmological parameters using subhaloes catalogues will be useful for more refined samples like CMASS and LOWZ catalogues in the Baryon Oscillation Spectroscopic Survey in SDSS-III.