  The present article is a part of the study of solvable Leibniz algebras with
a given nilradical. In this paper solvable Leibniz algebras, whose nilradicals
is naturally graded $p$-filiform non-Lie Leibniz algebra $(n-p\geq4)$ and the
complemented space to nilradical has maximal dimension, are described up to
isomorphism. Moreover, among obtained algebras we indicate the rigid and
complete algebras
