A mathematic model is obtained for the description of soliton-effect compression of picosecond pulse in optical fibers with slowly decreasing dispersion. Numerical simulations show that, as compared with the case of conventional soliton-effect comptessor, the compressed pulse from this kind of compressor is much shorter with a much higher ark power when the decrement velocity of the fiber dispersion is appropriately controlled. Furthermore, the compressed pulse is pedestal free. Given input pulse, we found that the highest compression ratio correspond to an optimal decrement velocity of the fiber dispersion which relates not only to the initial peak power but also to the initial pulse width of the input pulse.