A quantization of a non-standard rational solution of CYBE forsl2is given explicitly. We obtain the quantization with the help of a twisting of the usual YangianY{sl2). This quantum object (deformed YangianYηξ(sl2)) is a two-parametric deformation of the universal enveloping algebraU(sl2[u]) of the polynomial current algebrasl2[u]. We consider the pseudotriangular structure onYηξ(sl2), the quantum doubleDYηξ(sl2), its the universal R-matrix and also the RTT-realization ofYηξ(sl2).