Adaptive demodulation (ADM) using rateless codes has been considered as an alternative solution for rate adaptive systems. In this paper, we shall propose a maximum a posteriori probability (MAP) based ADM algorithm to select the bits to demodulate rather than using decision regions set (DRS) as in conventional ADM systems. Its main difference is that our demodulated bit selection is implemented by evaluating all bits in the data packet instead of per symbol. Therefore, the probability of discarding incorrect bits will increase, resulting in bit error rate (BER) performance improvement. In addition, our developed technique can adjust the demodulated bits rate to any rational rate and can be easily applied to any modulation scheme. Various simulations show that our proposed MAP based ADM technique significantly outperforms the conventional ADM algorithm in term of BER.