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The equations of motion of a super non-Abelian T-dual sigma model on the Liesupergroup $(C^1_1+A)$ in the curved background are explicitly solved by thesuper Poisson-Lie T-duality. To find the solution of the flat model we use thetransformation of supercoordinates, transforming the metric into a constantone, which is shown to be a supercanonical transformation. Then, using thesuper Poisson-Lie T-duality transformations and the dual decomposition ofelements of Drinfel'd superdouble, the solution of the equations of motion forthe dual sigma model is obtained. The general form of the dilaton fieldssatisfying the vanishing $\beta-$function equations of the sigma models isfound. In this respect, conformal invariance of the sigma models built on theDrinfel'd superdouble $((C^1_1+A),I_{(2|2)})$ is guaranteed up to one-loop, atleast.

Solution of the equations of motion for a super non-Abelian sigma model in curved background by the super Poisson-Lie T-duality