In recent years, orthogonal chirp division modulation (OCDM) has gained attention as a robust communication waveform due to its strong resistance to both time-domain and frequency-domain interference. However, similar to orthogonal frequency division multiplexing (OFDM), OCDM suffers from a high peak-to-average power ratio (PAPR), resulting in increased hardware costs and reduced energy efficiency of the transmitter's power amplifiers. In this work, we introduce a novel unitary transform called the Generalized Discrete Fresnel Transform (GDFnT) and propose a new waveform based on this transform, named Generalized Orthogonal Chirp Division Modulation (GOCDM). In GOCDM, data symbols from the constellation diagram are independently placed in the Generalized Fresnel (GF) domain. We derive the GF-domain channel matrix for the GOCDM system under time-frequency doubly selective channels and leverages the sparsity of the GF-domain channel matrix to design an iterative receiver based on the message-passing algorithm. Simulation results demonstrate that GOCDM achieves better PAPR performance than OCDM without compromising bit error rate (BER) performance.