Currently researches on CORDIC(coordinate rotation digital computer) algorithm are mainly about 16-bit output accuracy, yet higher precision outputs are needed in areas like digital encryption and information security. If some regular methods are adopted to implement 32-bit CORDIC algorithm, problems like long output delay and huge hardware consumption will arise. The 32-bit CORDIC algorithm, with a compressed LUT(look-up table),was proposed in this paper. The improved design, with less circuit resources and 3 clock periods output delay, compressed and decomposed the LUT according to the inner iteration pattern,folded the range, re-coded the angle, and merged some iterations. Simulation indicates that the size of compressed LUT using fixed-point format is reduced to 1.78%, and the output delay periods are reduced from 8 to 3. Moreover the average of magnitude of output error is 2.3048×10-10. The improved design has some advantages such as less hardware consumption, higher precision and less output delay, and it is more applicable for modern communication occasions that demand for brilliant time-real performance and less hardware resources.