We have developed a compact X-ray source via inverse Compton scattering between an electron beam and a laser pulse stacked in an optical super-cavity at Laser Undulator Compact X-ray (LUCX) accelerator in KEK. The accelerator consists of a photo-cathode RF-gun and an S-band accelerating tube and now produces the multi-bunch electron beam with 100 bunches, 0.5nC bunch charge and 40MeV beam energy. It is planned to upgrade the RF-gun and the RF system of the accelerator and the super-cavity in order to increase the X-ray yield. The new RF-gun with high mode separation and high Q value and a new klystron for the gun will be installed to provide good compensation with a high-intensity multi-bunch electron beam. A new optical super-cavity consisting of 4 mirrors is also being developed to enhance the stacking power in the cavity and to reduce the laser size at the focal point. The first targets are to produce a multi-bunch electron beam with 3000 bunches, 0.5nC bunch charge and 5MeV beam energy in low energy mode and with 100 bunches, 2nC and 40 MeV in high energy mode to generate X-rays by inverse Compton scattering. In this paper, the status and future plan of the accelerator will be reported.