The interaction and compression of the similariton beam generated in a mode-locked similariton laser system and compressed in a DDF (dispersion-decreasing fiber) with negative dispersion is investigated in this paper. First, a quality factor R is established to evaluate the quality of compressed similariton beams to design optimum tapered DDF. The result shows that the hyperbolically tapered DDF can achieve a best R compared to the linearly tapered DDF, exponentially tapered DDF, Gaussian tapered DDF, cosinoidally tapered DDF and logarithmically tapered DDF. Then, a pedestal energy ratio PE and a compression quality parameter Q are further established to evaluate the quality of compressed output beams considering the pulses with and without interaction by adjusting the time-delay q0 between the pulse pairs in a hyperbolically tapered DDF. Finally, we obtain the optimum compressed pulse pair both considering q0 = 4ps and q0 = 2.6ps, the pedestal energy ratios are 3.0048% and 13.4306%, maximum compression quality parameters are 454.3059 and 293.1326, the corresponding FWHM and peak power are 177.3fs and 302.2695W, 189.7fs and 249.4017W, respectively, demonstrating efficient and high-quality similariton beam compression.