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We present a three-dimensional Chern-Simons gravity based on a deformation of the Maxwell algebra. Such symmetry allows %\textcolor{blue}{introducing}to introduce a non-vanishing torsion to the Maxwell Chern-Simons theory, whose action contains the Mielke-Baelker model as a sub case for particular values of the coupling constants. By considering suitable boundary conditions, we show that the asymptotic symmetry is given by the $\widehat{\mathfrak{bms}}_3\oplus\mathfrak{vir}$ algebra with three independent central charges.
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