An improved COordinate Rotation DIgital Computer(CORDIC) algorithm based on a small-capacity read-only memory and detection of a few-bit positions detection is presentedproposed. In the design of the phase-amplitude module and phase accumulator，the angle-rotator judgment is was eliminated，and the method ofa binary-to-bipolar re-encoding method for the angle iswas used to reduce the residual angle calculations. Additionally，offset pre-rotation is was utilized employed to simplify the calculation of scale factors computation，and the number of rotations and system delay is were minimizedreduced by throughusing a few-bit detection algorithm. A direct digital frequency synthesizer(DDS)implemented based onusing this algorithm can generate 32 different distinct sine wave outputs，with a sine wave precision error less thanbelow 1. 4 × 10.6 . Compared with traditional CORDIC algorithms， the proposed algorithm method improveds power consumption，resource utilization，frequency resolution and area， achieving an spurious-free dynamic range(SFDR)of approximately 86. 2 dBc. Experimental results based on the ALINX AXU15EG FPGA platform show demonstrated that the output delay of this circuit structure didoes not exceed 20 ns，making itconfirming that the proposed design is faster and occupiesying fewer less area resources than other conventional CORDIC algorithm structures.