The power spectrum of the two-degree Field Galaxy Redshift Survey (2dFGRS) sample is estimated with the discrete wavelet transform (DWT) method. The DWT power spectra within 0.035<k<2.2 h Mpc⁻¹ are measured for three volume-limited samples defined in consecutive absolute magnitude bins −19∼−18, −20∼−19 and −21∼−20. We show that the DWT power spectrum can effectively distinguish ΛCDM models of σ₈ = 0.84 and σ₈ = 0.74. We adopt maximum likelihood method to perform three-parameter fitting of the bias parameter b, pairwise velocity dispersion σ_pv and redshift distortion parameter β = Ω_m^0.6/b to the measured DWT power spectrum. The fitting results state that in a σ₈ = 0.84 universe the best-fit values of Ω_m given by the three samples are mutually consistent within the range 0.28∼0.36, and the best fitted values of σ_pv are 398⁺³⁵₋₂₇, 475⁺³⁷₋₂₉ and 550±20 km s⁻¹ for the three samples, respectively. In the model of σ₈ = 0.74, our three samples give very different values of Ω_m. We repeated the fitting using the empirical formula of redshift distortion. The result of the model of low σ₈ is still poor, especially, one of the best-fit values of σ_pv is as large as 10³ km s⁻¹. We also repeated our fitting by incorporating a scale-dependent galaxy bias. This gave a slightly lower value of Ω_m. Differences between the models of σ₈ = 0.84 and σ₈ = 0.74 still exist in the fitting results. The power spectrum of 2dFGRS seems to disfavor models with low amplitude of density fluctuations if the bias parameter is assumed to be scale independent. For the fitting value of Ω_m to be consistent with that given by WMAP3, strong scale dependence of the bias parameters is needed.