In this paper, we put constraints on neutrino properties such as mass m_ν and degeneracy parameters ξ_i from WMAP5 data and light element abundances by using a Markov chain Monte Carlo (MCMC) approach. In order to take consistently into account the effects of the degeneracy parameters, we run the Big Bang Nucleosynthesis code for each value of ξ_i and the other cosmological parameters to estimate the Helium abundance, which is then used to calculate CMB anisotropy spectra instead of treating it as a free parameter. We find that the constraint on m_ν is fairly robust and does not vary very much even if the lepton asymmetry is allowed, and is given by ∑m_ν < 1.3 eV (95%C.L.).