Abstract: The super resolution spectral estimation can obtain higher resolution than conventional periodogram method In this paper a super resolution range and velocity estimation algorithm is presented, which is based on the state space method and proposed for moving target detection in linear frequency-modulated continuous wave(LFMCW) radar.This paper introduces the state space method and analyzes the characteristic of the upsweep and down-sweep beat signals of triangular LFMCW radar.Using the state space method the spectra of the beat signals are acquired Then according to the state space method the range and velocity estimation algorithm of moving targets is proposed This algorithm solves the problem of range-velocity decoupling; improves the range and velocity resolution and estimation precision of moving target in LFMCW radar. Simulation results prove the efficiency of the algorithm