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tokens: from the SDSS DR11 quasars at z = 2.34, we reconstruct the evolution of the dark energy EoS using the polynomial expansion, PCA, and the correlated prior method, respectively. In this paper, we pay attention to the high-redshift BAO measurement of BOSS DR11 quasars, the Ly α FB data, which have been widely used to constrain cosmological parameters (Lee et al. 2015 ; Delabrouille et al. 2015 ), especially the EoS of dark energy. However, we note that this measurement slightly prefers a negative dark energy density, so the second main purpose of this paper is to study the possible influence of this Ly α FB data on the constraints of the EoS of dark energy. In the next section, we show the numerical method and measurements used in this paper. Then, we use different reconstruction methods to explore the evolution of the dark energy EoS. In particular, we carefully check the impact of Ly α FB data on the results. The final section presents our conclusions and a discussion. 2. Method and Data We perform a global fitting analysis of cosmological parameters, using the CosmoMC package, 3 3 http://cosmologist.info/cosmomc/ a Markov Chain Monte Carlo (MCMC) code. We assume purely adiabatic initial conditions and a flat universe. Our parameterization is thus:the and are the baryon and cold dark matter physical densities, Θ s is the angular size of the sound horizon at decoupling, τ is the optical depth, n s and A s are the spectral index and the primordial power spectrum, and P w will be the parameters that describe dark energy. In order to understand the nature of dark energy well, we consider the following data sets. 2.1. SN As standard candles, the SN measurements provide a luminosity distance as a function of redshift z , making them a powerful probe for cosmology, particularly for the EoS of dark energy. In this paper, we use 740 samples from JLA (Betoule et al. 2014 ), in which the redshift spans 0 z 1.299, and there are only eight high-redshift samples ( z > 1). The absolute magnitude comes from the logarithm of the luminosity of an astronomical object seen from a 10 parsec distance, which can also be used to give its brightness. We use the distance modulus μ th to relate the expansion history of the universe to the apparent magnitude of an SN at a given redshift. It is defined as the difference between the apparent magnitude m and the absolute magnitude M of the SN and relates to the distance throughwith μ 0 = 42.38 and dimensionless D L = H 0 d L . The luminosity distance is given by d L = (1 + z ) r ( z ), with r ( z ) standing for the comoving distance: The observation of distance modulus μ obs is given by an empirical linear relation:where α and β are set to nuisance parameters in our numerical calculations, , x 1 , and are parameters describing the SN, and M B is related to the host stellar mass M stellar by a simple step function (Betoule et al. 2014 ):so we can calculate the χ 2 of SN following:where σ i is the error of i th SN sample.