The purpose of this work is to construct complete (k,n)-arcs in the projective 2-space PG(2,q) over Galois field GF(11) by adding some points of index zero to complete (k,n–1)arcs 3  n  11. A (k,n)-arcs is a set of k points no n + 1 of which are collinear. A (k,n)-arcs is complete if it is not contained in a (k + 1,n)-arc