As to the problem of difficulty in synchronization and demodulation of chaotic direct sequence spread spectrum (CD3S) signals, a demodulation algorithm for CD3S signals is proposed based on the dual extended Kalman filter joint estimation structure, taking advantage of the correlation between chaotic code synchronization and data symbol demodulation. The algorithm alternately conducts chaotic code estimation and data symbol estimation using dual extended Kalman filter structure, and accomplishes the synchronization and demodulation by joint estimation. Considering the degeneracy of Kalman gain caused by the mutual independence of data symbol state, the algorithm improves the calculation method of Kalman gain in the estimation of data symbol. Simulation results demonstrate that the algorithm can demodulate the CD3S signals correctly and the new Kalman gain calculation method helps to achieve better bit error rate performance.