In this letter, a novel Zadoff-Chu-orthogonal frequency division multiplexing (ZC-OFDM) waveform is designed for integrated communication and navigation (ICAN) in low Earth orbit (LEO) satellite systems. Firstly, the differential generalized ZC (DGZC) sequence is derived from the generalized ZC (GZC) sequence through differentially coherent processing to mitigate Doppler-induced ranging errors. Then, the DGZC sequence is integrated into ZC-OFDM to enable ICAN. Finally, an adaptive genetic algorithm (GA) is proposed for pilot assignment to obtain performance optimization with low complexity. Simulation results show that the proposed DGZC-OFDM system is capable of providing substantial performance gain over conventional ZC-OFDM counterpart in the terms of ranging accuracy and bit error ratio (BER).