The Maximum-A-Posteriori-probability (MAP) demodulation of recursive FQPSK-B in the presence of Additive White Gaussian Noise (AWGN) channel was first presented. Required in the iterative detection of Serial Concatenation of Convolutional coded Recursive FQPSK (SCCRFQPSK), the bit extrinsic Log-Likelihood Ratio (ex-LLR) of FQPSK demodulation was also derived. Secondly, aiming at weakening the phenomena of positive feedback during the iterative detection of SCCRFQPSK, the bit ex-LLR of FQPSK demodulation was appropriately adjusted by linear weighted processing. By Monte Carlo simulation, it was concluded that the optimal weighting factor of the weighted SCCRFQPSK system was 0.7, and it got 0.3dB Signal-to-Noise Ratio (SNR) gain at a Bit Error Rate (BRE) of 10-5 at 4 iterations. The simulation results indicate that the proposed method can not only accelerate the decoding convergence and improve the performance of the SCCRFQPSK system, but also reduce the delay. To a certain extent, it can deal with the deep space communication with low SNR caused by long distance.