Spectral mismatch between spectral profiles of two fiber Bragg gratings (FBGs) can deteriorate the fringe visibility of the constructed fiber Fabry-Perot (FFP) sensor system. Under the approximation of Gaussian profiles to reflection spectra of weak fiber Bragg gratings, the expression describing fringe visibility variations induced by spectral mismatch is deduced. The curve of fringe visibility is measured in an interferometric FFP sensor system, which is in good agreement with the theoretical analysis. The investigation indicates that, side lobes in reflection spectra of FBGs have a big influence upon visibility variations caused by spectral mismatch. And from the spectral match point of view, the FFP sensor system based on Gaussian apodized gratings is superior compared with that on normal uniform gratings.