Adaptive modulation and coding (AMC) and incremental redundancy (IR) are two popular rate adaptive systems to improve system capacity, peak data rate and reliable coverage of transmission in wireless mobile communications suffering from time-varying channel conditions. Adaptive demodulation (ADM) using rateless codes has been considered as an alternative solution for these rate adaptive systems in order to avoid their resource consumptions. In ADM system, data stream is modulated with a fixed modulation scheme at the transmitter but it is demodulated at a non-fixed rate at the receiver. If the signal to noise ratio (SNR) of the communication channel is not high enough to demodulate the message to reach predefined bit error rate (BER), demodulation level is then decreased by treating some of the bits in each symbol as erasures and being discarded. In this paper, we shall propose a log-likelihood ratio (LLR) based ADM algorithm to select the bits to demodulate. In our algorithm we shall select the bits to demodulate in whole information packet by comparing their probability to be correct instead of using modified constellation diagram to select bits per symbol. Therefore, the probability of discarding incorrect bits will increase, resulting in BER performance and transmission rate improvement. In addition, our developed algorithm can be applied easily to any modulation scheme and the corresponding demodulation rate can be selected as any rational rate value which relaxes the limitation of ADM systems. Various simulations show that our proposed LLR based ADM technique significantly outperforms the conventional ADM algorithm in term of BER performance.