A MAP (Maximum A posteriori Probability) receiver is described that is designed for Markovian sources in a wireless environment. A MAP receiver, a well-known efficient receiver, uses the stochastic characteristics of the source in the decision procedure. However, it is very difficult to implement a MAP algorithm at the front of the receiver because of its calculation costs. To reduce these costs we introduce a source predictor in the receiver. With the aid of the predictor, the MAP detector can be operated with a small calculation cost. Experimental PCM (Pulse Coded Modulation) image transmission demonstrated the feasibility of the proposed receiver. Simulation of the receiver's performance showed it had better MSE (Mean Squared Error) performance in spite of its implementation simplicity.