Summary form only given. Overlapping multi-pulse pulse position modulation (OMPPM) is a modulation scheme to achieve a higher throughput than other conventional modulation schemes. Ohtsuki, Sasase and Mori (see Conf. Rec. ICC'93, p.1123-1127, 1993) analyzed OPPM in a noiseless photon counting channel and showed that it outperforms other conventional modulations. The optical channel is often modeled by a noiseless photon counting channel, but noise due to background and/or detector dark currents exists in a practical optical channel. However, the performance of OMPPM in a noisy photon counting channel has not been clarified. The article analyzes the cutoff rate performance of OMPPM in a noisy photon counting channel.