The percolation problem for the 2-D triangular lattice of the quenched-correlated system is studied by using real-space renormalization group method. The many-body correlations for the occupied sites are considered by Kirkwood's superposition approximation approach and those for occupied and unoccupied sites by a procedure which holds the conservation of probability. The scheme is applied to the case including 3-body correlation and to that with next nearest neighboring correlations. Our conclusion is that, in either case the universality in critical phenomena of percolation ia unchanged, even some complicated correlations are involved.