A new concept of compound symbolic chaotic series is proposed. According to the kneading pair series in symbolic dynamics, by compounding a pseudo-random series with sub-series on condition of kneading rules we obtain a new symbolic chaotic series which is then transformed into a pseudo-random binary number (PRN) series. The length of the new PRN series elongates at a speed of geometric procession with iteration number. Theoretical and experimental analyses both prove that the above algorithm provides an effective PRN generator. To apply the algorithm to digital secure communication, a new cellular automata is established. With the automata, the data expansion is avoided, the encryption is finished quickly, the obvious avalanche effect can be produced, and thus the security is improved.