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The authors developed a useful analysis method of the rotational-angle of gear under transient state using the Hilbert Transform because the conventional method was not available under the transient state. Here, under the transient state the gear revolution speed was changed from 600r/min to 2000r/min in 0.35 seconds. A key technology of this method was that Hilbert Transform method, which used to be applicable only for steady data was improved so that it could treat transient data. Hence, the following procedures were developed. 1. The rotation of gear-teeth was detected by a gap-sensor pair, which can cancel the measuring error due to fluctuation of gear shaft. 2. The frequency of such signals varied significantly by the gear-revolution speed. Transient gear-teeth detection signals obtained at a constant sampling rate were converted to almost-constant frequency signals over the data series axis using a trigger pulse obtained per gear revolution.