The gradient pressure and temperature are unified into gradient density, the characteristics of femtosecond filamentation is investigated and the plasma channel in gases with gradient density is accompanied, the feasibility of gradient density method to enlarge the length of the filament and plasma channel is studied. Furthermore, the concept of ideal density curve is presented. The ideal shapes of gradient density under different conditions are calculated and analysized. The femtosecond pulses which propagate under the ideal gradient density curve can achieve the maximum spectra broadening and shorter pulses after compression while avoiding the muti-filament. It is found that the nature of intense femtosecond pulses propagation under the ideal density curve is in the condition of maintain constant n2Pc, to make the spot radius of the pulse at certain range in the long distance propagation, and to perform a self-guide while avoiding the self focusing or ionization.