The theoretical model of the hole mobility in poly[2-methoxy-5-(2'-ethylhexyloxy)p-phenylene vinylene] doped with a photochromic polar additive is proposed. Our model involves description of the on-chain charge carrier states, charge carrier thermalization, and inter-chain hopping. While the on-chain states are calculated by means of quantum mechanical methods, the semi-classical Marcus approach is used for the description of inter-chain hopping. The dependence of the mobility on several parameters of the model is studied. The results predict the possibility to construct an efficient optoelectronic switch based on a polymer doped with a photochromic polar additive.