Mutual compensation property between electrooptic and magnetooptic modulations in a crystal with electrooptic and magnetooptic effects and its application to magnetooptic sensor are investigated theoretically and experimentally. Under the condition of light intensity modulation, electrooptic and magnetooptic modulation effects can compensate for each other, so that the transmitted light intensity through the crystal can be kept at a certain fixed value. Based on this mutual compensation property, a novel optical current (or magnetic field) sensor is proposed and demonstrated experimentally by use of a single bismuth germanate (Bi4Ge3O12, BGO) crystal. The optical sensing unit is composed mainly of two polarizers and a block of BGO crystal with the shape of parallelogram. The BGO crystal itself can produce an optical phase bias of π/2, and it can be used as both a current sensing element and an electrooptic compensator. The change of magnetooptic rotation angle through the crystal can be compensated in real time by the change of electrooptic phase retardation caused by the applied voltage, thus the closed-loop optical measurement of current (or magnetic field) can be achieved. The 50 Hz ac current within 5 A is measured experimentally. The required compensating ac voltage is about 21.2 V/A in root-mean-square value. Experimental data show a good linear relationship between measured current and compensating voltage, and the nonlinear error is less than 1.7%.