A long-range Domany-Kinzel (1981) model proposed by Wu and Stanley (1982) is solved using random-walk formulations. In this model, for every site (i,j) in a two-dimensional lattice there is a directed bond present from site (i,j) to (i+1,j) with probability one. There are also m+1 directed bonds present from (i,j) to (i-k, j+1), k=-1, 0, 1, 2, 3...m-1 with respective probabilities pk+1 where m is any positive integer. An exact expression is obtained to determine the critical percolation angle theta c for any distribution of pn. The system percolates in the region theta c> theta >or=0 with probability one and zero outside this region where theta is the angle measured from the x axis. If the authors let m go to infinity and pn varies as p1n-s, they find that when s<or=2, theta c= pi . A closed form expression of theta c is obtained for s>or approximately=2. When m is large but finite, theta c is also obtained for the following two distributions: (a) pn=a/(a+n) with a>0, (b) pn= beta /m and beta >0.