A new class of nilpotent algebras called completable nilpotent Lie algebras was found dur- ing the study of complete Lie algebras. Although some completable nilpotent Lie algebras, as nilpotent Lie algebras of maximal rank and Heisenberg algebra, were found, there are many completable nilpotent Lie algebras unknown. The purpose of this thesis is to look for com- pletable nilpotent Lie algebras and investigate their structure. The first chapter is devoted to a class of 3-step nilpotent Lie algebras called quasi L3- filiform Lie algebras. It is shown that every Lie algebra N of this class is completable and DerN is a solvable complete Lie algebra when dimc2N = 1. In chapter 2 we consider the quasi Ln-filiform Lie algebras. We prove that quasi Ln-filiform Lie algebras are completable, explicitly determine the derivation algebra, automorphism group of quasi Ln-filiform Lie algebras, and applying some properties of root vector decomposition we obtain isomorphism theorem of quasi Ln-filiform Lie algebras. In chapter 3 we consider the quasi Qn-filiform Lie algebras. We prove that quasi Qn-filiform Lie algebras are completable, explicitly determine the derivation algebra, automorphism group of quasi Qn-filiform Lie algebras, and applying some properties of root vector decomposition we obtain isomorphism theorem of quasi Qn-filiform Lie algebras. The final chapter is devoted to the automorphism groups of solvable complete Lie algebras.We determine the automorphism groups of solvable complete Lie algebras, whose nilpotent radical is a quasi Heisenberg algebra, a quasi Ln-filiform Lie algebra, respectively.