In this paper, we use the renormalisation group approach and Monte-Carlo simulation to treat the problem of percolation on a two-dimensional square lattice with next-nearest-neighbour interactions. The critical probability pc and the critical exponents α,β,γ and so forth are obtained. It is shown that the two-dimensional percolation problem with next-nearest-neighbour interactions belongs to different universality class from that only with nearest-neighbour interactions.