We report a current scaling study of a quantum phase transition between a quantum anomalous Hall insulator and a trivial insulator on the surface of a heterostructure film of magnetic topological insulators. The transition was observed by tilting the magnetization while measuring the Hall conductivity σxy. The transition curves of σxy taken under various excitation currents cross each other at a single point, exemplifying a quantum critical behavior of the transition. The slopes of the transition curves follow a power-law dependence of the excitation current, giving a scaling exponent. Combining with the result of the previous temperature scaling study, critical exponents ν for the localization length and p for the coherence length are separately evaluated as ν=2.8±0.3 and p=3.3±0.3.