Abstarct: Linear complementary dual (LCD) codes are linear codes satisfying C∩C^⊥={O}.Researchers have proved that any linear codes over finite fields F_q (q>3), is equivalent to Euclidean LCD codes. Hence, the study of LCD code is mainly open for binary and ternary fields. In this thesis, we study new constructions of binary and ternary LCD codes by using matrix-product codes and prove that binary and ternary LCD codes from matrix-product codes are asymptotically good. Then we construct some new and good binary and ternary LCD codes using matrix-product codes. The Matrix-product LCD codes constructed in this thesis have very good parameters and contain some optimal codes.