The estimation errors on the spatial acoustic field using different order acoustic pressure gradient combinations were analyzed mathematically, and the effect of the inconsistency between the amplitude and phase in the differential channel on the finite difference approximation errors was calculated. The constraints of the self-noise of the hydrophone and the quantization error of analog-to-digital conversion on the lower limit of the operating frequency of the high-order hydrophone were studied. A high-order acoustic pressure gradient hydrophone composed of four piezoelectric bimorphs was proposed. The size of the hydrophone is 100 mm×50 mm, capable of measuring the first-order acoustic pressure gradient and the second-order mixed acoustic pressure gradient in the sound field. The output voltage of each channel of the hydrophone in the plane wave sound filed were obtained by finite element simulation. The calculated results show that the output voltage response of the second-order mixed pressure gradient channel increases by 12 dB per octave, and the directivity is consistent with that of the longitudinal quadrupole acoustic source.