In anomalous dispersivefiber, fundamental soliton pules have the desirable property i.e. their shape and pulsewidth are invariant during propagation along the fiber. In this paper, a new method tocompress fundamental soliton pulses in the anomalous dispersion regime throughcross-phase-modulation for pump pulse and soliton pulse is proposed. Two nonlinear coupledequations were established to describe the propagation of pulses in the fiber and solvednumerically. It is found that the fundamental soliton can be compressed by using themethod of the cross-phase modulation and exists an optimum value of fiber length in thecompression. It is also found that the pump pulse power, pump frequency chirp and variouspulse widths have great effects on soliton pulse compression. In order to obtain largecompression factor, pump pulses with negative chirp and narrow pulse-width are desirableselected.