Abstract: Quantum computers provide new opportunities for quantum chemistry. In this article,we present a versatile, extensible, and efficient software package, named Q²Chemistry, for developing quantum algorithms and quantum inspired classical algorithms in the field of quantum chemistry. In Q²Chemistry, the wave function and Hamiltonian can be conveniently mapped into the qubit space, then quantum circuits can be generated corresponding to a specific quantum algorithm already implemented in the package or newly developed by the users. The generated circuits can be dispatched to either a physical quantum computer, if available, or to the internal virtual quantum computer realized by simulating quantum circuits on classical computers. As demonstrated by our benchmark simulations, Q²Chemistry achieves excellent performance in simulating medium scale quantum circuits using the matrix product state algorithm. Applications of Q²Chemistry to simulate molecules and periodic systems are given with performance analysis.