Action calculi is introduced as a mathematical framework for expressing different interactive behaviors, which shows the advantages in representing different interactive models with some common features. In this paper, action calculi is used to include γ-calculus (a computational calculus for higher-order concurrent programming) in its setting. First, a concrete action calculus AC(K_γ) is defined. Then the formal compositional translation of the γ-calculus into AC(K_γ) is presented. Finally, upon definitions of the observability, the weak barbed bisimularity as well as the weak barbed congruence for AC(K_γ), it is proved that such translation preserves the weak behavioural equivalence of the γ-calculus with the π-calculus as intermediate. This work not only shows the expressiveness of action calculi, but also provides precondition for uniting and comparing γ-calculus with other concurrent models under the theory of action calculi.