There are three types in frequency response accelerometer; one is lightly damped piezp type, another is oil damping stainguage type and the third is electro induction type accelerometer within electromagnetic damping. The usable frequency range of lightly damped accelerometers is limited to 0.2 of their mounted natural frequency for amplitude distortion of less than 5 percents. There have been situation where the measured motion contains unforeseen high - frequency components, which are regarded as such due to the accelerometer transfer function. There are several way to overcome amplitude distortion of the higher than anticipated frequency components; (I) to make use of the accelerometer with natural frequency three times and more as high as the measured frequency, (II) to establish data-analysis techniques which will account for the amplitude distortion, (III) to set up a notch filter circuit which has a transfer function that is the reciprocal of the accelerometer transfer function, and so on. This paper makes a report of the method as to(III), i. e., set up a few notch filter circuits, it is discussed what happens when the transfer functions, are in discord as to natural frequency of the filter and accelerometer damping vs. filter damping. And especially as for the cantilever strain gauge type accelerometer made by oneself with ease, it was compared and discussed between the ideological value and the experimental value of actual designed circuit in case of the mismatching of the transfer functions, and it was considered whether to be practicable or not, the result of which was as following; the useful frequency range of the accelerometer can be extended to near resonance if (a) the accelerometer mounted natural frequency and the filter center frequency are matched within .+-. 2 percent and (b) the damping ratios are matched within two factors. Therefore, we obtained the good result in improvement for extending frequency response characteristics of accelerometer.