This paper presents a multiple-accessing chaotic digital communication system based on Interleaved Chaotic Differential Peaks Keying (I-CDPK) modulation technique. The proposed communication system consists of four major modules: Multiple-Accessing Chaotic Transmitter (MACT), Frequency modulation (FM) transmitter, FM receiver and Multiple-Accessing Chaotic Receiver (MACR). In this multiple-accessing chaotic digital communication system, the transmitted data of every Link are carried in a different state of the chaotic system instead of the using of chaotic sequences spreader or binary codes spreader, and only a scalar state variable (i.e. the output of MACT's chaotic circuit) is sent to the MACR's chaotic circuit through both FM transmitter and FM receiver. For synchronizing the chaotic circuits of the MACT and MACR, an observerbased chaotic synchronization scheme is used in this work. Besides, the Bit Detector in MACR is applied to recover the transmitted input digital bits corresponding to each individual Link. Some numerical simulations are executed for the illustrative communication system, which is a Rössler - like chaotic system. Moreover, the performance of bit error rate of the proposed system is compared with those of the correlator-based communication systems adopting coherent Binary Phase Shift Keying (BPSK) and coherent Differential Chaotic Shift Keying (DCSK) schemes.