Primordial gravitational waves generated by inflation have produced an odd-parity pattern B-mode in the cosmic microwave background (CMB) polarization. LiteBIRD (Light satellite for the studies of B-mode polarization and Inflation from cosmic background Radiation Detection) aims at detecting this B-mode polarization precisely. It requires about 2000 detectors capable of detecting a frequency range from 50GHz to 250GHz with ultra low noise. Superconducting detectors are suitable for this requirement. We have fabricated and tested microwave kinetic inductance detectors (MKIDs) and developed a new readout system. We have designed antenna-coupled MKIDs. Quasi-particles are created by incident radiation and are detected as a change of the surface impedance of a superconductor strip. This change of the surface impedance is translated into the change of the resonant frequency of a microwave signal transmitted through the resonator. We also have developed a new readout system for MKIDs. The newly developed readout system is not only able to read out the amplitude and the phase data with the homodyne detection for multi-channels, but also provides a unique feature of tracking the resonant frequency of the target resonator. This mechanism enables us to detect signals with a large dynamic range. We report on the recent R&D status of the developing MKIDs and on the read-out system for LiteBIRD.