The norm space is the pairs of vector space with defined norm in the vector space. An example of vector space is lp. Vector space lp is a space that contains all real number sequences that satisfy the sums of all elements in lp normed space. Furthermore at lp can be defined as a norm-2 ||.,.||p, that is equal to the sum of all 2 dimensional matrix determinant in norms in lp, such that (lp,||.,.||p) is a 2-normed space. Result of this study is seeking at the completeness of 2-normed space (lp,||.,.||p) by utilizing the completeness of norm space (lp,||.||p).