Maximally flat digital differentiators (MFDDs) are widely used in many applications. By using MFDDs, we obtain the derivative of an input signal with high accuracy around their center frequency of flat property. Moreover, to avoid the influence of noise, it is desirable to attenuate the magnitude property of MFDDs expect for the vicinity of the center frequency. In this paper, we introduce a design method of linear phase FIR band-pass MFDDs with an arbitrary center frequency. The proposed transfer function for both of TYPE III and TYPE IV can be achieved as a closed form function using Jacobi polynomial. Furthermore, we can easily derive the weighting coefficients of the proposed MFDDs using recursive formula. Through some design examples, we confirm that the proposed method can adjust the center frequency arbitrarily and the band width having flat property.