Abstract: Kelley studied Moors-smith convergence in a topological space and showedthat the topology of a space can be described completely in terms of convergence. relationships among the complete subset, Moors-smith convergence and Cartan Filter convergence in a complete lattice are investigated. Several theorems are obtained. The equivalence of the interior operator and the complete subset are studied. Moors-smithconvergence and Filter convergence, Moor-smith convergence and the complete subset are discussed. As a result, the complete subset finally got is practically equivalent with theconvergence. Thus Kelley's conclusion is extended to the complete lattices and theresults got by our predecessors are improved.