In order to solve the phase demodulation problem caused by cyclic jump, an automatic phase unwrapping algorithm based on field-programmable gate array (FPGA) was proposed. Using the data pipeline structure, the number of jump cycles was automatically found by the state machine, and the automatic phase compensation was realized by the number of jump cycles. The proposed algorithm was theoretically analyzed and verified by experiments. The results show that when the width of the counting bit of the jump cycle number is 8 bits, the FPGA can be applicable to the situation of less than 256 jumps. When the digital width of the jump cycle number increases, more jumps are applicable. The automatic phase unwrapping algorithm almost does not occupy storage resources, and can solve the arctangent phase jump problem caused by the increase of the vibration modulation range. The phase demodulation error is within 1‰, which meets the real-time requirements of high-precision vibration detection. The automatic phase unwrapping algorithm provides a more concise solution to the problem of cyclic jump in the calculation results of arctangent phase in laser Doppler vibration measurement.