Double stranded DNA can adopt different forms, the so-called A-, B-, and Z-DNA, which play different biological roles. In this work, the thermodynamic and the kinetic parameters for the base-pair closing and opening in A-DNA and B-DNA were calculated by all-atom molecular dynamics simulations at different temperatures. The thermodynamic parameters of the base pair in B-DNA were in good agreement with the experimental results. The free energy barrier of breaking a single base stack results from the enthalpy increase ΔH caused by the disruption of hydrogen bonding and base-stacking interactions, as well as water and base interactions. The free energy barrier of base pair closing comes from the unfavorable entropy loss ΔS caused by the restriction of torsional angles and hydration. It was found that the enthalpy change ΔH and the entropy change ΔS for the base pair in A-DNA are much larger than those in B-DNA, and the transition rates between the opening and the closing state for the base pair in A-DNA are much slower than those in B-DNA. The large difference of the enthalpy and entropy change for forming the base pair in A-DNA and B-DNA results from different hydration in A-DNA and B-DNA. The hydration pattern observed around DNA is an accompanying process for forming the base pair, rather than a follow-up of the conformation.