We propose an optical spread-time code-division multiple-access (ST-CDMA) with pulse position modulation (PPM) signaling for high-speed communication networks. We obtain a union upper bound on the bit error rate (BER) considering the multi-access interference (MAI), shot noise and thermal noise at the receiver. As a result, we show that the optical ST-CDMA with PPM signaling improves the BER performance at the same received power and bit rate compared to that with OOK signaling. This leads to an increase of the bit rate at the same BER. Moreover, we show that the proposed system can relax the requirement for spectral resolution compared to the optical ST-CDMA with OOK signaling under the received power and bit rate constraints.