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Assume the mapping $$A:\left\{  \begin{array}{ll}  x_{1}=x+\omega+y+f(x,y),  y_{1}=y+g(x,y),  \end{array}  \right. (x, y)\in \mathbb{T}^{d}\times B(r_{0}) $$ is reversible with respectto $G: (x, y)\mapsto (-x, y),$ and $| f | _{C^{\ell}(\mathbb{T}^{d}\timesB(r_{0}))}\leq \varepsilon_{0}, | g |_{C^{\ell+d}(\mathbb{T}^{d}\timesB(r_{0}))}\leq \varepsilon_{0},$ where $B(r_{0}):=\{|y|\le r_0:\; y\in\mathbbR^d\},$ $\ell=2d+1+\mu$ with $0<\mu\ll 1.$ Then when$\varepsilon_{0}=\varepsilon_{0}(d)>0$ is small enough and $\omega$ isDiophantine, the map $A$ possesses an invariantS torus with rotationalfrequency $\omega.$ As an application of the obtained theorem, the Lagrangestability is proved for a class of reversible Duffing equation with finitesmooth perturbation.

KAM theorem for reversible mapping of low smoothness with application