We propose and experimentally demonstrate a novel protocol for transferring quantum states between superconducting cavities. This approach utilizes continuous two-mode squeezing interactions to generate entanglement without the exchange of any carrier photons. In contrast to the discrete operations of entanglement and Bell-state measurement in quantum teleportation, our scheme is symmetric and continuous. We experimentally realize coherent and bidirectional transfer of arbitrary quantum states, including bosonic quantum error correction codes. Our results offer new insights into the quantum state transfer and quantum teleportation. In particular, our demonstration validates a new approach to realize quantum transducers and might find applications in a wide range of physical platforms.