Fluctuation of pump power is one of the major sources of temporal and intensity noise in femtosecond fiber lasers. In this work, the transfer functions between the relative intensity noise (RIN) of the pump laser diode (LD) and the output RIN, between the RIN of the pump LD and timing jitter of femtosecond fiber lasers are systematically studied. It is demonstrated, for the first time to our knowledge, that the amplitude of the pump RIN transfer function can be effectively decreased by an intra-cavity narrow band-pass filter. In particular, for normal-dispersion lasers, the 3-dB bandwidth of the transfer function can also be narrowed by two-thirds, with a steeper falling edge. Furthermore, with the narrow band-pass filtering, the transfer function is almost independent of the net intra-cavity dispersion due to amplifier similariton formation. The proposed scheme can effectively isolate the pump-induced noise without the need of complex active pump LD control and intra-cavity dispersion management, thus providing an easy way for practical high-power, high-stability femtosecond fiber laser design and related high-precision applications outside the laboratory.