This paper introduces Genesis, the first compiler designed to support Hamiltonian Simulation on hybrid continuous-variable (CV) and discrete-variable (DV) quantum computing systems.Genesis is a two-level compilation system.At the first level, it decomposes an input Hamiltonian into basis gates using the native instruction set of the target hybrid CV-DV quantum computer.At the second level, it tackles the mapping and routing of qumodes/qubits to implement long-range interactions for the gates decomposed from the first level.Rather than a typical implementation that relies on SWAP primitives similar to qubit-based (or DV-only) systems, we propose an integrated design of connectivity-aware gate synthesis and beamsplitter SWAP insertion tailored for hybrid CV-DV systems.We also introduce an OpenQASM-like domain-specific language (DSL) named CVDV-QASM to represent Hamiltonian in terms of Pauli-exponentials and basic gate sequences from the hybrid CV-DV gate set.Genesis has successfully compiled several important Hamiltonians, including the Bose-Hubbard model, Z 2 -Higgs model, Hubbard-Holstein model, Heisenberg model and Electron-vibration coupling Hamiltonians, which are critical in domains like quantum field theory, condensed matter physics, and quantum chemistry.Our implementation is available at Genesis-CVDV-Compiler https://