Abstract. The main motive of this paper is to study the Bianchi Type-III cosmological model in the context of f(T) gravity. We construct some f(T) models for expalning the evolutionary behavior of equation of state parameter ω_DE and energy density ρ_DE^(*). These parameters are calculated in terms of |T/T₀| and redshift z. To solve the field equations of the theory we have used hybrid expansion law which shows a transition from decelerated phase to an accelerated phase in f(T) theory gravity. We discuss these cosmological parameters graphically by taking different values of redshift and EoS parameter. The crossing of phantom divide line can be seen in exponential and combined f(T) models whereas it can not be seen in logarithmic models.

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