We are proposing a compact neutron generator based on a Li beam driver. The proposed neutron generator comprises a laser ion source, a radio-frequency quadrupole linear accelerator (RFQ linac), a drift tube linac, and a target containing protons. In the generator, the lithium ion is used as a projectile instead of protons to utilize the kinematic focusing technique. The technique enables us to enhance the neutron flux without increasing the beam energy, which is important to develop a clean compact neutron generator. Moreover, the combination of a laser ion source and a RFQ linac with the direct plasma injection scheme will provide several tens of mA of a fully ionized lithium beam, which is much higher than that of conventional heavy ion sources comparable with proton drivers. Neutrons are generated by the nuclear reaction of the lithium ions and protons in the beam target. In this paper, we reported the current status of the development. For RFQ, we designed the RFQ rods to accelerate 40 mA of 7Li3+. We fabricated and installed the rods into a cavity, and, as a first test, accelerated 10 mA of C6+ successfully.