The critical properties of a quenched site-correlated percolation system is treated by real-space renormalization group method. We chose the nearest-neighbour short-range order a as the correlation parameter. By treating the correlated probability self-consistently, we found, in two dimension, there is only one nontrivial physical fixed point and the correlation is an irrelevant parameter at random percolation fixed point, which is consistent with other correlated percolation models.