To solve the problems that pipelined coordinate rotation digital computer (CORDIC) algorithm has low output precision, long output time, and large hardware resource consumption, this paper proposes a bi-directional prediction scaling-free CORDIC algorithm. First, the algorithm decomposes the input angle in [0, π/4) into the smaller angle of 2^-i according to the bit value i after binary encoding of the angle. Then it uses the set-up lookup table to perform two-way scaling-free factor rotation based on the initial angle. It is not necessary to judge the next rotation direction according to the intermediate iteration result, which avoids the uncertainty of the iteration direction, reduces the number of iteration units and iterations, and improves the calculation accuracy. Finally, the algorithm transforms [π/4,2π) to [0, π/4) through the angle interval folding technique, so that the calculation interval is extended to the entire circumference [0,2π), which guarantees the calculation range. In addition, the algorithm can be achieved by only using shift and addition and subtraction operations, avoiding multiplication operations. Simulation and verification were carried out on MATLAB and Vivado. Results show that compared with the pipelined and unidirectional scaling-free CORDIC algorithms, when the output bit width was 14 bits, the output accuracy was increased by 47.5% and 18.8% respectively, the maximum output delay was reduced by 53.8% and 40.0% respectively, and the hardware resource consumption was improved to some extent. The algorithm has the characteristics of high output accuracy and short output delay, and its comprehensive performance has been greatly improved.