A novel turbo coded modulation scheme, called the turbo-APPM, for deep space optical communications is proposed. The proposed turbo-APPM is a serial concatenation of turbo codes, an accumulator and a pulse position modulation (PPM), where turbo codes act as an outer code while the accumulator and the PPM act together as an inner code. The generator polynomial and the puncturing rule for generating turbo codes are chosen to lower the bit error rate. At the receiver, the joint iterative decoding is performed between the inner decoder and the outer turbo decoder. In the outer decoder, local iterative decoding for turbo codes is conducted. Simulation results are presented showing that the proposed turbo-APPM outperforms all previously proposed schemes such as LDPC-APPM, RS-PPM and SCPPM reported in the literature.