In the continuous tuning process of the electric tunable liquid crystal Fabry-Perot filter (LCFPF), the phenomenon of the jumping of the transmission peak spectrums is found. And this phenomenon influences the monotone tuning performance of the device. Analysis for this phenomenon shows that it's due to the change of the interference order of Fabry-Perot cavity in the tuning process. And the relationship between the transmission peak wavelength λ, the interference order m, and the index n of the medium in the Fabry-Perot cavity is given, as well as the effective tuning range of the device. When the length of the cavity is 10 μm, the tuning range will cover the whole C Band with the index difference of only 0.05. The experimental result is in agreement with the numeric simulation. At last, some approaches are presented in order to improve the monotone tuning performance of the device.