Raman soliton self-frequency shift (SSFS) of ultrashort pulses propagating in a dispersion-decreasing fiber (DDF) was studied by using adiabatic perturbation method. An expression for Raman SSFS in DDF was obtained. The results show that there exists a threshold of the rate of the fiber dispersion decrease for the suppression of SSFS of solitons propagating in DDF. Only when the rate of the fiber dispersion decrease is larger than the threshold, the SSFS can be suppressed in the DDF. When the rate of the fiber dispersion decrease is l...