A novel parallel Laguerre blind equalization algorithm for common data link (CDL) is proposed to overcome the problems of traditional algorithms such as long tap coefficients and the high bit error rate (BER) for deep fading channels. By analyzing CDL signals, the new algorithm replaces FIR filter with Laguerre filter so as to approach longpulse response sequence with shorter tap coefficients. Meanwhile, the convergence is accelerated by using the decisiondirected algorithm and fractionally spaced structure. The selfadaptive step module directly adopts the expected value from the square of equalized output as a modified variable to further promote its equalization effect. The experimental results show that the proposed method can accelerate convergence and reduce BER in short tap coefficients.