The concept of normal subalgebras in \textit{B}- algebras is due to J. Neggers and H. S. Kim. We give an equivalent definition and show that the center Z(\textbf{A}) of a \textit{B}-algebra% \textbf{\ A }is a normal subalgebra of \textbf{A}. Moreover, we prove that the notion of a normal subalgebra is equivalent to the normal subgroup of the derived group. Hence the lattices of normal subalgebras (and also the congruence lattices) of \textit{B}-algebras are modular.