We give a new partially observable discrete time Markov decision model with general state and action spaces, under a fractional discounted criterion. In order to discuss an optimal policy for this model, by using the parametric method we transform this model to a partially observable Markov decision model under the usual discounted criterion, which is moreover transformed to the equivalent completely observable Markov decision model by using Bayes’s formula and the notion of an information policy. The existence, uniqueness and the continuity property of the solution of the optimality equation, and the optimal value function related our model are discussed.