To solve the problem of multivariate time-delay synchronous selection on phase space reconstruction(PSR), a maximal independent cross-correlation(MICC) algorithm was proposed to select multivariate phase space reconstruction time-delays. Firstly, the response variate sequence was segmented, and then, the segment surfaces were fitted and the observational sequences were substituted into the fitting function. At last, the optimal time-delay was computed iteratively when the cross-correlation was minimal. The simulation results of the Lorenz system were used to compare the binary and ternary time-delay selections of MICC algorithm with genetic neural networks, maximal entropy algorithm and mutual information algorithm. Joint recurrence plot(JRP) and mutual nearest neighbor radio(MNNR) were applied to evaluate the selections, and MICC algorithm was superior to the others. Besides, the coal mine gas concentrations of four crucial undermine locations were chosen to be the one real coal mine system coupling variates. The contrast experiments between MICC and mutual information had been done and the time-delays computed using MICC were 16-3-10-11 respectively, meanwhile the MNNR and JRP densities were 0.58 and 0.34%. The results showed that the MICC algorithm had obvious advantages in selecting optimal time-delays of multivariate and could be applied on multivariate analysis in practical issues.